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Medientyp:
E-Artikel
Titel:
On rational points of varieties over local fields having a model with tame quotient singularities
Beteiligte:
Hartmann, Annabelle
Erschienen:
American Mathematical Society (AMS), 2015
Erschienen in:
Transactions of the American Mathematical Society, 367 (2015) 11, Seite 8199-8227
Sprache:
Englisch
DOI:
10.1090/s0002-9947-2015-06291-6
ISSN:
1088-6850;
0002-9947
Entstehung:
Anmerkungen:
Beschreibung:
We study rational points on a smooth variety X X over a complete local field K K with algebraically closed residue field, and models X \mathcal {X} of X X with tame quotient singularities. If X \mathcal {X} is the quotient of a Galois action on a weak Néron model of the base change of X X to a tame Galois extension of K K , then we construct a canonical weak Néron model of X X with a map to X \mathcal {X} , and examine its special fiber. As an application we get examples of singular models X \mathcal {X} such that there are K K -rational points of X X specializing to a singular point of X \mathcal {X} . Moreover we obtain formulas for the motivic Serre invariant and the rational volume, and the existence of K K -rational points on certain K K -varieties with potential good reduction.