IHES

Mathematician John T. Tate died aged 94

It is with great sadness that the Institute learned of the passing, at age 94, of American mathematician John Torrent Tate. He was known worldwide for his work in number theory and algebraic geometry.

His influence in these areas is reflected in the many concepts bearing his name: Tate torsion, Tate-Shafarevich group, Tate module, Tate algebras, Tate cohomology, Tate duality theorem, Tate trace, Hodge-Tate theory, and Sato-Tate conjecture, are some examples.

After completing a master’s degree in mathematics at Harvard University and a PhD at Princeton on “Fourier analysis in number fields and Hecke’s zeta function”, under the supervision of Emil Artin, Tate taught at Harvard for 36 years. In 1990, he joined the University of Texas at Austin, from which he retired in 2009.

Throughout his career, John T. Tate has developed strong connections with the French mathematical community. From the 1950s, and for about ten years, he was part of the Bourbaki group. He gave seminars at Collège de France and was a visiting professor at IHES on several occasions. He is co-author, together with J.-P. Serre, of the theory that now bears their names, the Serre-Tate theory. From the 1950s onwards, they maintained a long scientific correspondence, which was partly published in 2015 by the Société mathématique de France.

One episode in particular relates his theory of rigid analytical spaces to the Institute. In 1962 IHES circulated Tate’s text on rigid geometry, at the request of J.-P. Serre but without his agreement. The text was then published in the mathematical journal Inventiones Mathematicae and served as a basis for the development of rigid geometry. Tate came up with the idea that his p-adic uniformization of elliptic curves indicated the existence of a general theory of p-adic analytical spaces. This idea was so radically new that even Grothendieck was very sceptical at first, changing his mind once Tate began to develop his theory in 1961 [1].

Since 1992 John T. Tate was an associate foreign member of the Academy of Sciences. He was also a member of the National Academy of Sciences, the American Mathematical Society, the Norwegian Academy of Sciences and Humanities, and an honorary member of the London Mathematical Society.

In 2010 he was awarded the Abel Prize, one of the two most prestigious awards in mathematics, for “his vast and lasting impact on the theory of numbers“. The Wolf Prize (2002), the Steele Prize (1995), and the Cole Prize in Number Theory (1956), are some of the several other honors he received throughout his career.

The IHES extends its deepest condolences to his family.

 

[1] J.S. Milne, The work of John Tate, arXiv:1210.7459, p.28