Constancy of generalized Hodge-Tate weights of a local system
Number Theory
2019-02-20 v1 Algebraic Geometry
Abstract
Sen attached to each p-adic Galois representation of a p-adic field a multiset of numbers called generalized Hodge-Tate weights. In this paper, we discuss a rigidity of these numbers in a geometric family. More precisely, we consider a p-adic local system on a rigid analytic variety over a p-adic field and show that the multiset of generalized Hodge-Tate weights of the local system is constant. The proof uses the p-adic Riemann-Hilbert correspondence by Liu and Zhu, a Sen-Fontaine decompletion theory in the relative setting, and the theory of formal connections. We also discuss basic properties of Hodge-Tate sheaves on a rigid analytic variety.
Keywords
Cite
@article{arxiv.1710.08888,
title = {Constancy of generalized Hodge-Tate weights of a local system},
author = {Koji Shimizu},
journal= {arXiv preprint arXiv:1710.08888},
year = {2019}
}