World Library  
Flag as Inappropriate
Email this Article

John Tate

Article Id: WHEBN0000245933
Reproduction Date:

Title: John Tate  
Author: World Heritage Encyclopedia
Language: English
Subject: Emil Artin, Wolf Prize in Mathematics, In the news/Candidates/March 2010, Benedict Gross, Dinesh Thakur (mathematician)
Collection: 1925 Births, 20Th-Century American Mathematicians, 21St-Century American Mathematicians, Abel Prize Laureates, Fellows of the American Mathematical Society, Guggenheim Fellows, Harvard University Alumni, Harvard University Faculty, Living People, Members of the French Academy of Sciences, Members of the Norwegian Academy of Science and Letters, Members of the United States National Academy of Sciences, Nicolas Bourbaki, Number Theorists, People from Minneapolis, Minnesota, Princeton University Alumni, University of Texas at Austin Faculty, Wolf Prize in Mathematics Laureates
Publisher: World Heritage Encyclopedia
Publication
Date:
 

John Tate

John Tate
Born John Torrence Tate, Jr.
(1925-03-13) March 13, 1925
Minneapolis, Minnesota, USA
Nationality American
Fields Mathematics
Institutions Princeton University (1950–1953)
Columbia University (1953–1954)
Harvard University (1954–1990)
University of Texas, Austin (1990–2009)
Alma mater Harvard University (A.B., 1946)
Princeton University (Ph.D., 1950)
Doctoral advisor Emil Artin
Doctoral students Ki-Seng Tan
V. Kumar Murty
Edward Assmus
Theodore Chinburg
Benedict Gross
Jonathan Lubin
Stephen Lichtenbaum
Kenneth Alan Ribet
Joseph H. Silverman
Dinesh Thakur
Jerrold Tunnell
Robert Warfield
Carl Pomerance
George Bergman
Known for Tate conjecture
Tate module
Influenced John H. Coates
Notable awards Abel Prize (2010)
Wolf Prize (2002/03)
Steele Prize (1995)
Cole Prize in Number Theory (1956)

John Torrence Tate, Jr. (born March 13, 1925) is an American mathematician, distinguished for many fundamental contributions in algebraic number theory, arithmetic geometry and related areas in algebraic geometry. He is professor emeritus at Harvard University. He was awarded the Abel Prize in 2010.

Contents

  • Biography 1
  • Mathematical work 2
  • Awards and honors 3
  • Selected publications 4
  • See also 5
  • References 6
  • External links 7

Biography

Tate was born in Minneapolis. His father, John Tate Sr., was a professor of physics at the University of Minnesota, and a longtime editor of Physical Review. His mother, Lois Beatrice Fossler, was a high school English teacher. Tate Jr. received his bachelor's degree in mathematics from Harvard University, and entered the doctoral program in physics at Princeton University. He later transferred to the mathematics department and received his PhD in 1950 as a student of Emil Artin. Tate taught at Harvard for 36 years before joining the University of Texas in 1990. He retired from the Texas mathematics department in 2009, and returned to Harvard as a professor emeritus. He currently resides in Cambridge, Massachusetts with his wife Carol. He has three daughters with his first wife Karin Tate.[1]

Mathematical work

Tate's thesis (1950) on Fourier analysis in number fields has become one of the ingredients for the modern theory of automorphic forms and their L-functions, notably by its use of the adele ring, its self-duality and harmonic analysis on it; independently and a little earlier, Kenkichi Iwasawa obtained a similar theory. Together with his teacher Emil Artin, Tate gave a cohomological treatment of global class field theory, using techniques of group cohomology applied to the idele class group and Galois cohomology.[2] This treatment made more transparent some of the algebraic structures in the previous approaches to class field theory which used central division algebras to compute the Brauer group of a global field.

Subsequently Tate introduced what are now known as Tate cohomology groups. In the decades following that discovery he extended the reach of Galois cohomology with the Poitou–Tate duality, the Tate–Shafarevich group, and relations with algebraic K-theory. With Jonathan Lubin, he recast local class field theory by the use of formal groups, creating the Lubin–Tate local theory of complex multiplication.

He has also made a number of individual and important contributions to p-adic theory; for example, Tate's invention of rigid analytic spaces can be said to have spawned the entire field of rigid analytic geometry. He found a p-adic analogue of Hodge theory, now called Hodge–Tate theory, which has blossomed into another central technique of modern algebraic number theory.[2] Other innovations of his include the 'Tate curve' parametrization for certain p-adic elliptic curves and the p-divisible (Tate–Barsotti) groups.

Many of his results were not immediately published and some of them were written up by Serge Lang, Jean-Pierre Serre, Joseph H. Silverman and others. Tate and Serre collaborated on a paper on good reduction of abelian varieties. The classification of abelian varieties over finite fields was carried out by Taira Honda and Tate (the Honda–Tate theorem).[3]

The Tate conjectures are the equivalent for étale cohomology of the Hodge conjecture. They relate to the Galois action on the l-adic cohomology of an algebraic variety, identifying a space of 'Tate cycles' (the fixed cycles for a suitably Tate-twisted action) that conjecturally picks out the algebraic cycles. A special case of the conjectures, which are open in the general case, was involved in the proof of the Mordell conjecture by Gerd Faltings.

Tate has also had a major influence on the development of number theory through his role as a Ph.D. advisor. His students include Joe Buhler, Benedict Gross, Robert Kottwitz, Jonathan Lubin, Stephen Lichtenbaum, James Milne, V. Kumar Murty, Carl Pomerance, Ken Ribet, Ted Chinburg, Joseph H. Silverman, Dinesh Thakur, Jeremy Teitelbaum.

Awards and honors

In 1956 Tate was awarded the American Mathematical Society's Cole Prize for outstanding contributions to number theory. In 1995 he received the Leroy P. Steele Prize for Lifetime Achievement from the American Mathematical Society. He was awarded a Wolf Prize in Mathematics in 2002/03 for his creation of fundamental concepts in algebraic number theory.[4] In 2012 he became a fellow of the American Mathematical Society.[5]

In 2010, the Norwegian Academy of Science and Letters, of which he is a member,[6] awarded him the Abel Prize, citing "his vast and lasting impact on the theory of numbers". According to a release by the Abel Prize committee "Many of the major lines of research in algebraic number theory and arithmetic geometry are only possible because of the incisive contributions and illuminating insights of John Tate. He has truly left a conspicuous imprint on modern mathematics."[7]

Tate has been described as "one of the seminal mathematicians for the past half-century" by William Beckner, Chairman of the Department of Mathematics at the University of Texas.[1]

Selected publications

  • Tate, John (1950), Fourier analysis in number fields and Hecke's zeta functions ,  
  • Tate, John (1952), "The higher dimensional cohomology groups of class field theory", Ann. of Math. (2) 56: 294–297,  
  •  
  • Tate, John (1965), "Algebraic cycles and poles of zeta functions", Arithmetical Algebraic Geometry (Proc. Conf. Purdue Univ., 1963), New York: Harper & Row, pp. 93–110,  
  •  
  • Tate, John (1966), "Endomorphisms of abelian varieties over finite fields", Inventiones Mathematicae 2: 134–144,  
  • Tate, John (1967), "p-divisible groups", in Springer, T. A., Proceedings of a Conference on Local Fields, Springer-Verlag, pp. 158–183,  
  •  
  •  
  • Tate, John (1971), "Rigid analytic spaces", Inventiones Mathematicae 12: 257–289,  
  • Tate, John (1976), "Relations between K2 and Galois cohomology", Inventiones Mathematicae 36: 257–274,  
  • Tate, John (1984), Les conjectures de Stark sur les fonctions L d'Artin en s=0, Progress in Mathematics 47, Boston, MA: Birkhäuser Boston, Inc.,  

See also

References

  1. ^ a b c Ralph K.M. Haurwitz (March 24, 2010). "Retired UT mathematician wins prestigious Abel Prize". Statesman.com. 
  2. ^ a b "American mathematician John Tate wins 2010 Abel Prize". Xinhua.net. 2010-03-25. 
  3. ^ J.T. Tate, "Classes d'isogénie des variétés abéliennes sur un corps fini (d' après T. Honda)" , Sem. Bourbaki Exp. 352 , Lect. notes in math. , 179 , Springer (1971)
  4. ^ The 2002/3 Wolf Foundation Prize in Mathematics. Wolf Foundation. Accessed March 24, 2010.
  5. ^ List of Fellows of the American Mathematical Society, retrieved 2013-08-25.
  6. ^ "Gruppe 1: Matematiske fag" (in Norwegian).  
  7. ^ Anne Marie Astad (ed.). "The Abel Prize". The Norwegian Academy of Science and Letters. 
  • Milne, J, "The Work of John Tate" [2]

External links

This article was sourced from Creative Commons Attribution-ShareAlike License; additional terms may apply. World Heritage Encyclopedia content is assembled from numerous content providers, Open Access Publishing, and in compliance with The Fair Access to Science and Technology Research Act (FASTR), Wikimedia Foundation, Inc., Public Library of Science, The Encyclopedia of Life, Open Book Publishers (OBP), PubMed, U.S. National Library of Medicine, National Center for Biotechnology Information, U.S. National Library of Medicine, National Institutes of Health (NIH), U.S. Department of Health & Human Services, and USA.gov, which sources content from all federal, state, local, tribal, and territorial government publication portals (.gov, .mil, .edu). Funding for USA.gov and content contributors is made possible from the U.S. Congress, E-Government Act of 2002.
 
Crowd sourced content that is contributed to World Heritage Encyclopedia is peer reviewed and edited by our editorial staff to ensure quality scholarly research articles.
 
By using this site, you agree to the Terms of Use and Privacy Policy. World Heritage Encyclopedia™ is a registered trademark of the World Public Library Association, a non-profit organization.
 



Copyright © World Library Foundation. All rights reserved. eBooks from World eBook Library are sponsored by the World Library Foundation,
a 501c(4) Member's Support Non-Profit Organization, and is NOT affiliated with any governmental agency or department.