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arXiv · 1710.08888

Constancy of generalized Hodge-Tate weights of a local system

Koji Shimizu
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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.

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Koji Shimizu. 2017-10-24. Constancy of generalized Hodge-Tate weights of a local system. https://doi.org/10.1112/s0010437x1800742x

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