is a Japanese mathematician. He grew up in the prefecture of

Wakayama Wakayama may refer to: *Wakayama Prefecture, a prefecture of Japan *Wakayama (city) Wakayama City Hall is the capital city of Wakayama Prefecture in the Kansai region of Japan. , the city had an estimated population of 351,391 in 157066 househol ...

Japan Japan ( ja, 日本, or , and formally , ''Nihonkoku'') is an island country in East Asia. It is situated in the northwest Pacific Ocean, and is bordered on the west by the Sea of Japan, while extending from the Sea of Okhotsk in the north ...

. He attended college at the

University of Tokyo , abbreviated as or UTokyo, is a public research university located in Bunkyō, Tokyo, Japan. Established in 1877, the university was the first Imperial University and is currently a Top Type university of the Top Global University Project by ...

, from which he also obtained his master's degree in 1975, and his PhD in 1980. He was a professor at

Tokyo University , abbreviated as or UTokyo, is a public research university located in Bunkyō, Tokyo, Japan. Established in 1877, the university was the first Imperial University and is currently a Top Type university of the Top Global University Project by ...

Tokyo Institute of Technology is a national research university located in Greater Tokyo Area, Japan. Tokyo Tech is the largest institution for higher education in Japan dedicated to science and technology, one of first five Designated National University and selected as ...

and

Kyoto University , mottoeng = Freedom of academic culture , established = , type = National university, Public (National) , endowment = ¥ 316 billion (2.4 1000000000 (number), billion USD) , faculty = 3,480 (Teaching Staff) , administrative_staff ...

. He joined the faculty of the

University of Chicago The University of Chicago (UChicago, Chicago, U of C, or UChi) is a private research university in Chicago, Illinois. Its main campus is located in Chicago's Hyde Park neighborhood. The University of Chicago is consistently ranked among the b ...

in 2009. He has contributed to

number theory Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic function, integer-valued functions. German mathematician Carl Friedrich Gauss (1777� ...

and related parts of

algebraic geometry Algebraic geometry is a branch of mathematics, classically studying zeros of multivariate polynomials. Modern algebraic geometry is based on the use of abstract algebraic techniques, mainly from commutative algebra, for solving geometrical ...

. His first work was in the higher-dimensional generalisations of

local class field theory In mathematics, local class field theory, introduced by Helmut Hasse, is the study of abelian extensions of local fields; here, "local field" means a field which is complete with respect to an absolute value or a discrete valuation with a finite re ...

using algebraic K-theory. His theory was then extended to higher global class field theory in which several of his papers were written jointly with Shuji Saito. He contributed to various other areas such as ''p''-adic Hodge theory, logarithmic geometry (he was one of its creators together with

Jean-Marc Fontaine Jean-Marc Fontaine (13 March 1944 – 29 January 2019) was a French mathematician. He was one of the founders of p-adic Hodge theory. He was a professor at Paris-Sud 11 University from 1988 to his death. Life In 1962 Fontaine entered the Écol ...

and

Luc Illusie Luc Illusie (; born 1940) is a French mathematician, specializing in algebraic geometry. His most important work concerns the theory of the cotangent complex and deformations, crystalline cohomology and the De Rham–Witt complex, and logarithmic ...

), comparison conjectures, special values of zeta functions including applications to the Birch-Swinnerton-Dyer conjecture, the

Bloch-Kato conjecture on Tamagawa numbers In mathematics, the study of special values of L-functions is a subfield of number theory devoted to generalising formulae such as the Leibniz formula for pi, namely :1 \,-\, \frac \,+\, \frac \,-\, \frac \,+\, \frac \,-\, \cdots \;=\; \frac,\! ...

, and

Iwasawa theory In number theory, Iwasawa theory is the study of objects of arithmetic interest over infinite towers of number fields. It began as a Galois module theory of ideal class groups, initiated by (), as part of the theory of cyclotomic fields. In the ea ...

. A special volume of Documenta Mathematica was published in honor of his 50th birthday, together with research papers written by leading number theorists and former students it contains Kato's song on Prime Numbers. In 2005 Kato received the

Imperial Prize of the Japan Academy The is a prestigious honor conferred to two of the recipients of the Japan Academy Prize. Overviews It is awarded in two categories: humanities and natural sciences. The Emperor and Empress visit the awarding ceremony and present a vase to ...

for "Research on Arithmetic Geometry".

Books

Kato has published several books in Japanese, of which some have already been translated into English. He wrote a book on

Fermat's Last Theorem In number theory, Fermat's Last Theorem (sometimes called Fermat's conjecture, especially in older texts) states that no three positive integers , , and satisfy the equation for any integer value of greater than 2. The cases and have been k ...

and is also the coauthor of the two volumes of the trilogy on Number Theory, which have been translated into English.

References

{{DEFAULTSORT:Kato, Kazuya 20th-century Japanese mathematicians 21st-century Japanese mathematicians Number theorists 1952 births Living people People from Wakayama Prefecture University of Tokyo alumni Kyoto University faculty University of Tokyo faculty Tokyo Institute of Technology faculty University of Chicago faculty Laureates of the Imperial Prize Fellows of the American Academy of Arts and Sciences