On variation of Hodge-Tate structures
type: Item
instance of: scholarly article
title: On variation of Hodge-Tate structures
zbMATH Open document ID: 0645.14002
DOI: 10.1007/BF01443501
author: Osamu Hyodo
published in: Mathematische Annalen
publication date: 1989-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/164536
review text: This paper develops a formalism of variation of Hodge-Tate structures. The theory of Hodge-Tate structure was introduced by Tate as a p-adic analogue of classical Hodge theory. Faltings has found the so-called Hodge-Tate decomposition, which may be considered as a p-adic counterpart of classical Hodge decomposition concerning the cohomology group of the constant sheaf. To generalize this to the cohomology groups of local systems, the notion ``Hodge-Tate'' is introduced for a smooth \({\mathbb{Q}}_ p\)-sheaf on a smooth variety over a p-adic field. Then a result concerning stability is obtained. Namely, it is shown that the higher direct image of a Hodge-Tate sheaf by a proper smooth morphism is still a Hodge-Tate sheaf.
Mathematics Subject Classification ID: 14C30
Mathematics Subject Classification ID: 14F05
zbMATH DE Number: 4051771
zbMATH Keywords: variation of Hodge-Tate structures
zbMATH Keywords: stability
zbMATH Keywords: Hodge-Tate sheaf
MaRDI profile type: Publication
cites work: Notes on Crystalline Cohomology. (MN-21)
cites work: Hodge-Tate structures and modular forms
cites work: p-Adic Hodge Theory
cites work: Q3866210
cites work: Formes différentielles et modules de Tate des variétés abéliennes sur les corps locaux. (Différential forms and Tate modules of abelian varieties over local fields)
cites work: Q3769025
cites work: On the Hodge-Tage decomposition in the imperfect residue field case.
cites work: On the differentiation of De Rham cohomology classes with respect to parameters
OpenAlex ID: W2068801259
description: scientific article; zbMATH DE number 4051771