ITEM METADATA RECORD
Title: A trace formula for varieties over a discretely valued field
Authors: Nicaise, Johannes # ×
Issue Date: 2011
Publisher: W. de Gruyter
Series Title: Journal für die Reine und Angewandte Mathematik (Crelle's Journal) vol:650 pages:193-238
Abstract: We study the motivic Serre invariant of a smoothly bounded algebraic or rigid variety X over a complete discretely valued field K with perfect residue ¯eld k. If K has characteristic zero, we extend the de¯nition to arbitrary K-varieties using Bittner's presentation of the Grothendieck ring and a process of N¶eron smoothening of pairs of varieties.
The motivic Serre invariant can be considered as a measure for the set of unramified points on X. Under certain tameness conditions, it admits a cohomological interpretation by means of a trace formula. In the curve case, we use T. Saito's geometric criterion for cohomological tameness to obtain more detailed results. We discuss some applications to Weil-Chatelet groups,
Chow motives, and the structure of the Grothendieck ring of varieties.
ISSN: 0075-4102
Publication status: published
KU Leuven publication type: IT
Appears in Collections:Non-KU Leuven Association publications
× corresponding author
# (joint) last author

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