On Rational Points of Varieties over Local Fields having a Model with Tame Quotient Singularities
Abstract
We study rational points on a smooth variety X over a complete local field K with algebraically closed residue field, and models of X with tame quotient singularities. If a model of X is the quotient of a Galois action on a weak N\'eron model of the base change of X to a tame Galois extension of K, then we construct a canonical weak N\'eron model of X with a map to this model, and examine its special fiber. As an application we get examples of singular models of X such that X has K-rational points specializing to a singular point of this model. Moreover we obtain formulas for the motivic Serre invariant and the rational volume, and the existence of K-rational points on certain K-varieties with potential good reduction.
Keywords
Cite
@article{arxiv.1212.5039,
title = {On Rational Points of Varieties over Local Fields having a Model with Tame Quotient Singularities},
author = {Annabelle Hartmann},
journal= {arXiv preprint arXiv:1212.5039},
year = {2015}
}
Comments
26 pages; to appear in Trans. Amer. Math. Soc., minor changes