Higher local and global class field theory was developed by A. Parshin, Kazuya Kato, Ivan Fesenko, Spencer Bloch, Shuji Saito and other mathematicians.
He contributed to p-adic Hodge theory, logarithmic geometry (he was one of its creators together with Jean-Marc Fontaine and Luc Illusie), comparison conjectures, special values of zeta functions including the Birch-Swinnerton-Dyer conjecture and Bloch-Kato conjecture on Tamagawa numbers, Iwasawa theory, and many others.
Higher dimensional class field theory was pioneered by A.N. Parshin in positive characteristic and K. Kato, I. Fesenko, Sh.
Its statement was previously known as the Bloch–Kato conjecture, after Spencer Bloch and Kazuya Kato, or more precisely the motivic Bloch–Kato conjecture in some places, since there is another Bloch–Kato conjecture on values of L-functions.
Together with Coates, Fukaya, Kato, and Venjakob she formulated a non-commutative version of the main conjecture of Iwasawa theory, on which much foundation of this important subject is based.
Kato Olympos | Kato Hideki | Sonoko Kato | Kazuya Kato | Kato | Kazuya Kuroda | Joji Kato | Shigeaki Kato | Ryozo Kato | Kato's conjecture | Kato Nevrokopi | Kato Kaelin | Kató Havas | Yasunori Katō | Takeshi Kato | Miliyah Kato | Masato Kato | Masaru Kato | Koichi Kato | Kenzo Kato | Kazuya Hiraide | Kazuhiko Kato (musician) | Kazuhiko Kato | Kato Hiroyuki | Kato (Green Hornet) | Kato (DJ) | Daisuke Katō | Ai Kato |