19 citations · 50 across the 15 of their papers we have counts for
8 papers · 1 filter
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…
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…
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…
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…