On rational points of varieties over local fields having a model with tame quotient singularities

Hartmann, Annabelle

doi:10.1090/S0002-9947-2015-06291-6

On rational points of varieties over local fields having a model with tame quotient singularities
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by Annabelle Hartmann PDF

Trans. Amer. Math. Soc. 367 (2015), 8199-8227 Request permission

Abstract:

We study rational points on a smooth variety $X$ over a complete local field $K$ with algebraically closed residue field, and models $\mathcal {X}$ of $X$ with tame quotient singularities. If $\mathcal {X}$ 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 $\mathcal {X}$, and examine its special fiber. As an application we get examples of singular models $\mathcal {X}$ such that there are $K$-rational points of $X$ specializing to a singular point of $\mathcal {X}$. 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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