22 citations · 80 across the 37 of their papers we have counts for
12 papers · 1 filter
Upper Ramification Groups for Arbitrary Valuation Rings
Kazuya Kato, Vaidehee Thatte
T. Saito established a ramification theory for ring extensions locally of complete intersection. We show that for a Henselian valuation ring with field of fractions and for…
Height functions for motives, II
Kazuya Kato
This is the Part II of our paper "Height functions for motives". We consider more general period domains and the height functions on more general sets of motives. We also consider…
Height functions for motives
Kazuya Kato
We define various height functions for motives over number fields. We compare these height functions with classical height functions on algebraic varieties, and also with analogous…
Compactifications of S-arithmetic quotients for the projective general linear group
Takako Fukaya, Kazuya Kato, Romyar Sharifi
Let F be a global field, and let S be a finite set of places of F containing all archimedean places. Consider the product X of the symmetric spaces and Bruhat-Tits buildings for PG…
Modular symbols and the integrality of zeta elements
Takako Fukaya, Kazuya Kato, Romyar Sharifi
We consider modifications of Manin symbols in first homology groups of modular curves with p-adic integer coefficients for an odd prime p. We show that these symbols generate homol…
Modular symbols in Iwasawa theory
Takako Fukaya, Kazuya Kato, Romyar Sharifi
This survey paper is focused on a connection between the geometry of and the arithmetic of over global fields, for integers . For $d =…