19 citations · 50 across the 15 of their papers we have counts for
15 papers
Arithmetic monodromy of hyper-Kähler varieties over -adic fields
Kazuhiro Ito, Tetsushi Ito, Teruhisa Koshikawa +2
In this paper, we study the -adic and -adic monodromy operators associated with hyper-Kähler varieties over -adic fields, in connection with Looijenga-Lunts-Verbitsky L…
Inequalities characterizing distinguished unipotent orbits
Alexander Bertoloni Meli, Teruhisa Koshikawa, Jonathan Leake
In this paper we prove a new characterization of the distinguished unipotent orbits of a connected reductive group over an algebraically closed field of characteristic 0. For class…
Logarithmic prismatic cohomology II
Teruhisa Koshikawa, Zijian Yao
We continue to study the logarithmic prismatic cohomology defined by the first author, and complete the proof of the de Rham comparison and étale comparison generalizing those of B…
The Hodge standard conjecture for self-products of K3 surfaces
Kazuhiro Ito, Tetsushi Ito, Teruhisa Koshikawa
As an application of our previous work on CM liftings of K3 surfaces and the Tate conjecture, we prove the Hodge standard conjecture for squares of K3 surfaces. We also deduce the…
Relative -cohomology
Ildar Gaisin, Teruhisa Koshikawa
We construct a relative version of the -cohomology theory developed by Bhatt-Morrow-Scholze and relate it to the prismatic theory of Bhatt-Scholze. The construction re…
The numerical Hodge standard conjecture for the square of a simple abelian variety of prime dimension
Teruhisa Koshikawa
We prove the numerical Hodge standard conjecture for the square of a simple abelian variety of prime dimension, and also in some related cases.
Eichler-Shimura relations for local Shimura varieties
Teruhisa Koshikawa
In this note, we discuss several forms of the Eichler-Shimura relation for the compactly supported cohomology of local Shimura varieties, using the work of Fargues-Scholze.
On the generic part of the cohomology of local and global Shimura varieties
Teruhisa Koshikawa
Using the work of Fargues-Scholze, we prove a vanishing theorem for the generic unramified part of the cohomology of local Shimura varieties of general linear groups. This gives an…
Logarithmic Prismatic Cohomology I
Teruhisa Koshikawa
We introduce a logarithmic variant of the notion of -rings, which we call -rings, and use it to define a logarithmic version of the prismatic site introduced by Bhatt…
Vanishing theorems for the mod cohomology of some simple Shimura varieties
Teruhisa Koshikawa
We show that the mod cohomology of a simple Shimura variety treated in Harris-Taylor's book vanishes outside a certain nontrivial range after localizing at any non-Eisenstein i…
Galois representations associated with a non-selfdual automorphic representation of GL(3)
Tetsushi Ito, Teruhisa Koshikawa, Yoichi Mieda
In 1994, van Geemen and Top constructed a non-selfdual motive of rank three over conjecturally associated with a cuspidal non-selfdual automorphic representation of $\…
CM liftings of K3 surfaces over finite fields and their applications to the Tate conjecture
Kazuhiro Ito, Tetsushi Ito, Teruhisa Koshikawa
We give applications of integral canonical models of orthogonal Shimura varieties and the Kuga-Satake morphism to the arithmetic of K3 surfaces over finite fields. We prove every K…
The -cohomology in the semistable case
Kestutis Cesnavicius, Teruhisa Koshikawa
For a proper, smooth scheme over a -adic field , we show that any proper, flat, semistable -model of whose logarithmic de Rham cohomology…
Overconvergent unit-root F-isocrystals and isotriviality
Teruhisa Koshikawa
We show that a semisimple overconvergent "absolutely unit-root" F-isocrystal on a geometrically connected smooth variety over a finite field becomes constant over a finite covering…
On heights of motives with semistable reduction
Teruhisa Koshikawa
We study heights of motives with integral coefficients over number fields introduced by Kato. It is a generalization of the Faltings height of an abelian variety and we establish g…