1. Alexander Grothendieck Alexander Grothendieck. search on title find similar wiki printableversion wiki normal version GFDL Alexander Grothendieck http://brandt.kurowski.net/projects/lsa/wiki/view.cgi?doc=429

2. Alexander Grothendieck - Wikipedia, The Free Encyclopedia . Alexander Grothendieck. From Wikipedia, the free encyclopedia. Alexander Grothendieck ( born March 28, 1928 in Berlin), is one of the leading http://www.wikipedia.org/wiki/Alexander_Grothendieck

Alexander Grothendieck From Wikipedia, the free encyclopedia. Alexander Grothendieck (born March 28 in Berlin ), is one of the leading mathematicians of the twentieth century, with major contributions to algebraic geometry homological algebra , and functional analysis . He was awarded the Fields Medal in and coawarded the Crafoord Prize with Pierre Deligne in . He declined the latter prize on ethical grounds. Because of his mastery of abstract approaches to mathematics, but also because of the many stories told about his retirement and his alleged mental disorders, he is one of the most intriguing scientific personalities of the 20th century Table of contents showTocToggle("show","hide") 1 Mathematical achievements 1.1 Major mathematical topics (from Récoltes et Semailles) 2 Life 2.1 Childhood and studies ... edit Mathematical achievements Homological methods and sheaf theory had already been introduced in algebraic geometry by Jean-Pierre Serre , after sheaves had been invented by Jean Leray . Grothendieck took them to a higher level, changing the tools and the level of abstraction. Amongst his insights, he shifted attention from the study of individual varieties to the

3. Grothendieck Alexander Grothendieck. Born 28 March 1928 in Berlin, Germany. AlexanderGrothendieck s father was Russian and he was murdered by the Nazis. http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Grothendieck.html

Alexander Grothendieck Born: 28 March 1928 in Berlin, Germany Click the picture above to see a larger version Show birthplace location Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Main index Alexander Grothendieck In 1949 Grothendieck moved to the University of Nancy where he worked on functional analysis with . He became one of the Bourbaki group of mathematicians which included Weil Henri Cartan and . He presented his doctoral thesis Grothendieck spent the years 1953-55 at the University of Sao Paulo and then he spent the following year at the University of Kansas. However it was during this period that his research interests changed and they moved towards topology and geometry. In fact during this period Grothendieck had been supported by the Centre National de la Recherche Scientifique, the support beginning in 1950. After leaving Kansas in 1956 he therefore returned to the Centre National de la Recherche Scientifique. However in 1959 he was offered a chair in the newly formed Institut des Hautes Etudes Scientifiques which he accepted. In [2] the next period in Grothendieck's career is described as follows:- It is no exaggeration to speak of Grothendieck's years algebraic geometry , and him as its driving force. He received the

4. Alexander Grothendieck Alexander Grothendieck. Alexander lived with his father, a revolutionary named AlexanderShapiro, and his mother, Hanka Grothendieck, in Berlin until 1933. http://www.fact-index.com/a/al/alexander_grothendieck.html

Main Page See live article Alphabetical index Alexander Grothendieck Alexander Grothendieck (born March 28 in Berlin ), is one of the leading mathematicians of the twentieth century, with major contributions to algebraic geometry homological algebra , and functional analysis . He was awarded the Fields Medal in and Crafoord Prize in Table of contents 1 Mathematical achievements 1.1 Major mathematical topics (from Récoltes et Semailles) 2 Life 2.2 Childhood and studies ... 3 External links Mathematical achievements Homological methods and sheaf theory had already been introduced in algebraic geometry by Jean-Pierre Serre , after sheaves had be invented by Jean Leray . Grothendieck took them to a higher level, changing the tools and the level of abstraction. Amongst his insights, he shifted attention from the study of individual varieties to the relative point of view (pairs of varieties related by a morphism ), allowing a broad generalization of many classical theorems. This he applied first to the Riemann-Roch theorem , around 1954, which had already recently been generalized to any dimension by Hirzebruch). He adapted the use of non-closed ( generic ) points, which led to the theory of

5. Alexander Grothendieck - Encyclopedia Article About Alexander Grothendieck. Free encyclopedia article about Alexander Grothendieck. Alexander Grothendieck in Freeonline English dictionary, thesaurus and encyclopedia. Alexander Grothendieck. http://encyclopedia.thefreedictionary.com/Alexander Grothendieck

Dictionaries: General Computing Medical Legal Encyclopedia Alexander Grothendieck Word: Word Starts with Ends with Definition Alexander Grothendieck (born March 28 March 28 is the 87th day of the year in the Gregorian Calendar (88th in Leap years). There are 278 days remaining. Events 845 - Paris is sacked by Viking raiders, probably under Ragnar Lodbrok, who collects a huge ransom in exchange for leaving. 1776 - Juan Bautista de Anza finds the site for the Presidio of San Francisco. 1834 - The United States Senate censures President Andrew Jackson for his actions in defunding the Second Bank of the United States. Click the link for more information. Centuries: 19th century - 20th century - 21st century Decades: 1870s 1880s 1890s 1900s 1910s - Years: 1923 1924 1925 1926 1927 - Events January 10 - USSR expels Leon Trotsky February 11 - 1928 Winter Olympic Games open in St. Moritz, Switzerland February 25 - Charles Jenkins Laboratories of Washington, DC becomes the first holder of a television license from the Federal Radio Commission. Click the link for more information.

6. Alexander Grothendieck - Enciclopedia Libre Translate this page Alexander Grothendieck. Artículo de la Enciclopedia Libre Universalen Español. Alexander Grothendieck es un matemático judeo-franco http://enciclopedia.us.es/index.php/Alexander_Grothendieck

Enciclopedia Libre Universal en Español Cambios recientes Edita esta página Historial ... Aviso Legal No has entrado Registrarse/Entrar Ayuda Alexander Grothendieck Artículo de la Enciclopedia Libre Universal en Español Alexander Grothendieck es un matemático judeo-franco-alemán, nacido en Berlín el 28 de marzo de , que durante la segunda mitad del s. XX ha llevado a cabo un extraordinario proceso de unificación de la Aritmética, la Geometría Algebraica y la Topología, dando gran impulso al desarrollo de estas tres ramas fundamentales de las matemáticas. Su padre Alexander Schapiro (6 de agosto de 1890 ¿1942?) fue un anarquista ruso que participó en la revolución rusa de 1917. Huyendo de la persecución comunista, emigra a Berlín, donde conoció a Hanka Grothendieck ( Hamburgo , 21 de agosto de 1900 Montpellier , 16 de diciembre de 1957), mujer de vida fascinante, vida que narra en su novela inédita Eine Frau hasta la concepción del único hijo que tuvo con Schapiro: Alexander Grothendieck. En los años 1934-39 Grothendieck vive en Hamburgo con una familia adoptiva, mientras sus padres están en Francia y participan en la guerra civil española. En 1939 se reúne con su madre Hanka en Francia. En 1940, al ser alemanes, se le interna en el campo de Rieucros junto con su madre, y estudia en el cercano Instituto de Mende. Mientras, su padre es internado en el campo de Le Vernet, y fue deportado por los nazis en 1942 a Auchswitz, donde desapareció. En 1942 Grothendieck es acogido La Guespy, hogar infantil del Socorro Suizo para refugiados en Chambon sur Lignon, y termina el Bachillerato en el Collège Cévénol.

7. Alexander Grothendieck Alexander Grothendieck. Alexander žil s jeho otcem, revolucionár jmenoval AlexanderaShapira, a jeho matka, Hanka Grothendieck, v Berlín until 1933. http://wikipedia.infostar.cz/a/al/alexander_grothendieck.html

švodn­ str¡nka Tato str¡nka v origin¡le Alexander Grothendieck Alexander Grothendieck (narozen½ 28. března v Berl­n ), je jeden vedouc­ matematici dvac¡t©ho stolet­, s velk½mi př­spěvky k algebraick¡ geometrie homological algebra , a funkčn­ anal½za . On byl udělen Medaile pol­ v a Crafoord cena v Tabulka s obsahem showTocToggle (" přehl­dka ", " schov¡vat se ") 1 matematick© ºspěchy 1. 1 hlavn­ matematick¡ t©mata (od R � coltes et Semailles) 2 život 2. 2 dětstv­ a studia ... 3 vnějÅ¡­ spojen­ Matematick© ºspěchy Homological metody a svazek teorie už byla představena v algebraick© geometrii Jean-Pierre Serre , po svazky měly b½t vynalezen Jean Leray . Grothendieck vzal je k vyÅ¡Å¡­ ºrovni, měnit n¡stroje a ºroveň abstrakce. Mezi jeho nahl©dnut­, on přesunul pozornost od studie o individu¡ln­ch rozmanitostech k poměrn© hledisko (p¡ry rozmanitost­ př­buzn½ morphism ), dovolovat Å¡irok© zevÅ¡eobecňov¡n­ mnoho klasick½ch teor©mů. Toto on platil nejprve k Riemann-Roch teor©m , asi 1954, kter½ měl už ned¡vno been celkov½ k nějak©mu rozměru Hirzebruch).

8. Alexander Grothendieck - Wikipédia Translate this page Alexander Grothendieck. Un Alexander Grothendieck est un mathématicienfrançais, né le 28 mars 1928 à Berlin (Allemagne). Il http://fr.wikipedia.org/wiki/Alexander_Grothendieck

Alexander Grothendieck Un article de Wikip©dia, l'encyclop©die libre. Alexander Grothendieck est un math©maticien fran§ais , n© le 28 mars Berlin Allemagne ). Il est arriv© en France en , et   fait ses ©tudes   Montpellier puis   Nancy , aupr©s de Jean Dieudonn© et Laurent Schwartz , qui dirigeront sa th¨se. Apr¨s des travaux remarquables en analyse fonctionnelle, sujet de sa th¨se, il se tourne vers la g©om©trie alg©brique . Il r©volutionne ce domaine en ©tablissant de nouvelles fondations et introduit la notion de sch©ma. Il a re§u la m©daille Fields en . Il a refus© le Prix Crafoord en Il a contribu© de mani¨re exceptionnelle aux math©matiques contemporaines, dans des domaines tr¨s vari©s. modifier Voir aussi ‰l©ments de g©om©trie alg©brique Cette page est consid©r©e comme une ©bauche   compl©ter . Si vous poss©dez quelques connaissances sur le sujet, vous pouvez les faire partager en ©ditant d¨s   pr©sent cette page (en cliquant sur le lien « modifier » Views Article Discussion Modifier Historique Outils personnels Identification Navigation Accueil Portail communaut© Actualit©s Modifications r©centes ... Faire un don Rechercher Bo®te   outils Pages li©es Suivi des liens Pages sp©ciales Autres langues English Derni¨re modification de cette page : 6 mai 2004   01:50.

9. Alexander Grothendieck Definition Of Alexander Grothendieck In Computing. What I Computer term of Alexander Grothendieck in the Computing Dictionary andThesaurus. Provides search by definition of Alexander Grothendieck. http://computing-dictionary.thefreedictionary.com/Alexander Grothendieck

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10. Alexander Grothendieck Legal Definition Of Alexander Grothendieck. What Is Alexa Definition of Alexander Grothendieck in the Ledal Dictionary and Thesaurus. AlexanderGrothendieck. Word Word. http://legal-dictionary.thefreedictionary.com/Alexander Grothendieck

Dictionaries: General Computing Medical Legal Encyclopedia Alexander Grothendieck Word: Word Starts with Ends with Definition Alexander Grothendieck is not available in the legal dictionary. Try: encyclopedia You may also use the word browser links: Full Dictionary Browser Alexander Duff, 1st Duke of Fife (enc.) Alexander Dugin (enc.) Alexander Dumas (enc.) Alexander Dyce (enc.) Alexander Edmund Batson Davie (enc.) Alexander Elliott Anderson Salmond (enc.) Alexander Emanuel Agassiz (enc.) Alexander Ewing (enc.) Alexander F. Poleshchuk (enc.) Alexander Fedorovich Kerensky (enc.) Alexander Filipov (enc.) Alexander Fleming Alexander Fleming (enc.) Alexander Fleming House (enc.) Alexander Forrest (enc.) Alexander Frederick Douglas-Home, Baron Home of the Hirsel (enc.) Alexander Frumkin (enc.) Alexander G. McNutt (enc.) Alexander Galt (enc.) Alexander Gerschenkron (enc.) Alexander Glazounov (enc.) Alexander Glazunov (enc.) Alexander Gode (enc.) Alexander Godfrey (enc.) Alexander Godunov (enc.) Alexander Goehr (enc.) Alexander Gorodnitsky (enc.) Alexander Gottlieb Baumgarten (enc.)

11. Alexander Grothendieck Alexander Grothendieck. Alexander lived with his father, a revolutionary named AlexanderShapiro, and his mother, Hanka Grothendieck, in Berlin until 1933. http://www.sciencedaily.com/encyclopedia/alexander_grothendieck

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12. Encyclopedia4U - Alexander Grothendieck - Encyclopedia Article alexander grothendieck. His father, a revolutionary named Shapiro, died in Auschwitz.With his mother, Hanka grothendieck, alexander survived in Vichy France. http://www.encyclopedia4u.com/a/alexander-grothendieck.html

ENCYCLOPEDIA U com Lists of articles by category ... Encyclopedia Home Page SEARCH : Alexander Grothendieck Alexander Grothendieck (born March 28 in Berlin ), is one of the leading mathematicians of the twentieth century, with monumental contributions to functional analysis and then to algebraic geometry . He won the Fields Medal in Born to Jewish parents, he was a displaced person during much of his childhood due to the upheavals of World War II . His father, a revolutionary named Shapiro, died in Auschwitz . With his mother, Hanka Grothendieck, Alexander survived in Vichy France. After the war, young Grothendieck studied mathematics in France , initially at Montpellier ; he came to Paris in . He wrote his dissertation under Laurent Schwartz in functional analysis, from . He was at this time a leading expert in the theory of topological vector spaces. However he set this subject aside by in order to work in algebraic geometry and homological algebra Homological methods and sheaf theory had already been introduced in algebraic geometry by Jean Leray and by Jean-Pierre Serre , but Grothendieck took them to a higher level. Among his insights, he shifted attention from the study of varieties to pairs of varieties related by a morphism, allowing a great generalization of many classical theorems such as the

13. Grothendieck Biography of alexander grothendieck (19280BC) alexander grothendieck. Born 28 March 1928 in Berlin, Germany alexander grothendieck's father was Russian and he was murdered by the Nazis. grothendieck moved to France in 1941 and http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Grothendieck.html

Alexander Grothendieck Born: 28 March 1928 in Berlin, Germany Click the picture above to see a larger version Show birthplace location Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Main index Alexander Grothendieck In 1949 Grothendieck moved to the University of Nancy where he worked on functional analysis with . He became one of the Bourbaki group of mathematicians which included Weil Henri Cartan and . He presented his doctoral thesis Grothendieck spent the years 1953-55 at the University of Sao Paulo and then he spent the following year at the University of Kansas. However it was during this period that his research interests changed and they moved towards topology and geometry. In fact during this period Grothendieck had been supported by the Centre National de la Recherche Scientifique, the support beginning in 1950. After leaving Kansas in 1956 he therefore returned to the Centre National de la Recherche Scientifique. However in 1959 he was offered a chair in the newly formed Institut des Hautes Etudes Scientifiques which he accepted. In [2] the next period in Grothendieck's career is described as follows:- It is no exaggeration to speak of Grothendieck's years algebraic geometry , and him as its driving force. He received the

14. Encyclopedia4U - List Of Mathematical Topics (G-I) - Encyclopedia Article function Green, George Green s theorem Gregory, James Greibach normalform Grobner basis grothendieck, alexander grothendieck topology http://www.encyclopedia4u.com/l/list-of-mathematical-topics-g-i-.html

ENCYCLOPEDIA U com Lists of articles by category ... Encyclopedia Home Page SEARCH : List of mathematical topics (G-I) For the purpose and extent of this list, see list of mathematical topics A-C D-F - G-I - J-L M-O P-R S-U ... V-Z G G2 (mathematics) G-delta set Gabriel's horn Galilean transformation ... Gaussian quadrature Guassian rational Gauss-Jordan elimination Gauss-Legendre algorithm Gauss-Markov Gauss-Markov process ... Gauss's law Gauss-Wantzel theorem Gelfand-Naimark-Segal Gelfand representation General linear group General number field sieve ... Geometric shape Geometric solid Geometry Geometry of numbers Gergonne point Germain ... Gosset, William Sealey Gowers, William Timothy Graded algebra Gradient Gradient descent Graftals ... Guldin, Paul Gumbel, Eric H H infinity Haar integral Haar measure Haar wavelet ... Harmonic series (music) Harsanyi, John Hash function Hash table Hasse diagram Hausdorff, Felix ... Helix Hellman, Martin Heng, Zhang Henkin Henkin, Leon Henstock-Kurzweil Integral Henstock-Kurzweil-Stieltjes Integral Heptadecagon Herbrand, Jacques Herbrand theory Herbrand universe Hereditarily finite set Charles Hermite Hermite polynomials ... Hessian Hestenes, David

15. Grothendieck Portrait alexander grothendieck. JOC/EFR September 2003 The URL of this pageis © Copyright information. http//wwwhistory.mcs.st-andrews http://www-gap.dcs.st-and.ac.uk/~history/PictDisplay/Grothendieck.html

Alexander Grothendieck JOC/EFR September 2003 The URL of this page is: http://www-history.mcs.st-andrews.ac.uk/PictDisplay/Grothendieck.html

16. Résultats De La Recherche Translate this page Auteur grothendieck, alexander (13 articles) grothendieck Numdam grothendieck,alexander On the de Rham cohomology of algebraic varieties. http://www.numdam.org/numdam-bin/recherche?h=aur&aur=Grothendieck, Alexander&for

17. Papers SGA 6 (my translation, 1994) grothendieck, alexander. Classes of sheaves and the RiemannRoch theorem. Selections from Recoltes et Semailles. grothendieck, alexander. Les orphelins, etc http://www.math.fsu.edu/~aluffi/compr.html

Filed papers, and notes from talks Preprint, 1984 Abbena, Elsa; Grassi, Antonella Hermitian left invariant metrics on complex Lie groups and cosymplectic Hermitian manifolds Preprint Aberbach, Ian; Huneke, Craig A theorem of Briancon-Skoda type for regular local rings containing a field Ch. 2 in "Geometric Invariance in Computer Vision" Abhyankar, Shreeram Invariant Theory and Enumerative Combinatorics of Young Tableaux Ch. 2 in "Algebraic Geometry and its Applications" Abhyankar, Shreeram Square-root Parametrization of Plane Curves Current Science, 63, 5, 9/1992 Abhyankar, Shreeram Resolution of singularities in various characteristics Discrete Applied Math. 31 (1991) 81-96 Abhyankar, Shreeram; Chandrasekar, Srinivasan; Chandru, Vijaya Intersection of algebraic space curves J. Reine Angew. Math. 276 (1975) 149-166 Abhyankar, Shreeram; Moh Tzuong-tsieng Embeddings of the line in the plane Preprint, 1995 Abkulut, S. Lectures on Seiberg-Witten Invariants Talk, Univ. of Chicago, 5/28/97 Abramovich, Dan Stable reduction for fibred surfaces Lecture notes Abramovich, Dan

18. Résultats De La Recherche Translate this page 13 réponses grothendieck, alexander Résumé des résultats essentiels dans lathéorie des produits tensoriels topologiques et des espaces nucléaires. http://www.numdam.org/numdam-bin/recherche?au=Grothendieck&format=short

19. A MAD DAYS WORK FROM GROTHENDIECK TO CONNES AND KONTSEVICH THE the present synthesis.alexander grothendieck dominated the rst ten years of the a very small geographical region. alexander. grothendiecks grandfather was probably a member http://www.ams.org/bull/2001-38-04/S0273-0979-01-00913-2/S0273-0979-01-00913-2.p

20. Grothendieck Topology At a time when cohomology for sheaves on topological spaces was well established,alexander grothendieck wanted to define cohomology theories for other http://www.fact-index.com/g/gr/grothendieck_topology.html

Main Page See live article Alphabetical index Grothendieck topology In mathematics , a Grothendieck topology is a structure defined on an arbitrary category C which allows the definition of sheaves on C , and with that the definition of general cohomology theories. A category together with a Grothendieck topology on it is called a site . This tool is used in algebraic number theory and algebraic geometry schemess , but also for flat cohomology and crystalline cohomology. Note that a Grothendieck topology is not a topology in the classical sense. History and idea At a time when cohomology for sheaves on topological spaces was well established, Alexander Grothendieck wanted to define cohomology theories for other structures, his schemess . He thought of a sheaf on a topological space as a "measuring rod" for that space, and the cohomology of such a measuring rod as a rough measure for the underlying space. His goal was thus to produce a structure which would allow the definition of more general sheaves or "measuring rods"; once that was done, the model of topological cohomology theories could be followed almost verbatim. Motivating example Start with a topological space X and consider the sheaf of all continuous real-valued functions defined on X . This associates to every open set U in X the set F U ) of real-valued continuous functions defined on U . Whenver U is a subset of V , we have a "restriction map" from F V ) to F U ). If we interpret the topological space

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