Potentially good reduction loci of Shimura varieties
Number Theory
2019-08-07 v2 Algebraic Geometry
Abstract
In this paper, we give a notion of the potentially good reduction locus of a Shimura variety. It consists of the points which should be related with motives having potentially good reductions in some sense. We show the existence of such locus for a Shimura variety of preabelian type. Further, we construct a partition of the adic space associated to a Shimura variety of preabelian type, which is expected to describe degenerations of motives. Using this partition, we prove that the cohomology of the potentially good reduction locus is isomorphic to the cohomology of a Shimura variety up to non-supercuspidal parts.
Keywords
Cite
@article{arxiv.1611.04839,
title = {Potentially good reduction loci of Shimura varieties},
author = {Naoki Imai and Yoichi Mieda},
journal= {arXiv preprint arXiv:1611.04839},
year = {2019}
}
Comments
54 pages. This article subsumes arXiv:1109.4697. Minor modifications