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arXiv · 1212.5039

On Rational Points of Varieties over Local Fields having a Model with Tame Quotient Singularities

Annabelle Hartmann
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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 Néron model of the base change of X to a tame Galois extension of K, then we construct a canonical weak Néron 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.

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Annabelle Hartmann. 2013-10-23. On Rational Points of Varieties over Local Fields having a Model with Tame Quotient Singularities. https://doi.org/10.1090/s0002-9947-2015-06291-6

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