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

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 n ...

. 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 b ...

, from which he also obtained his master's degree in 1975, and his

PhD PHD or PhD may refer to: * Doctor of Philosophy (PhD), an academic qualification Entertainment * '' PhD: Phantasy Degree'', a Korean comic series * '' Piled Higher and Deeper'', a web comic * Ph.D. (band), a 1980s British group ** Ph.D. (Ph.D. al ...

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 = Public (National) , endowment = ¥ 316 billion (2.4 billion USD) , faculty = 3,480 (Teaching Staff) , administrative_staff = 3,978 (Total Staff) , students = ...

. 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 integer-valued functions. German mathematician Carl Friedrich Gauss (1777–1855) said, "Ma ...

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 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, 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 th ...

. 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 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 ...

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