Title: A trace formula for rigid varieties, and motivic Weil generating series for formal schemes
Authors: Nicaise, Johannes # ×
Issue Date: Feb-2009
Publisher: Springer
Series Title: Mathematische annalen vol:343 issue:2 pages:285-349
Abstract: We establish a trace formula for rigid varieties X over a complete discretely valued field, which relates the set of unramified points on X to the Galois action on its etale cohomology. Next, we show that the analytic Milnor fiber of a morphism f at a point x completely determines the formal germ of f at x. We develop a theory of motivic integration for formal schemes of pseudo- finite type over a complete discrete valuation ring R, and we introduce theWeil generating series of a regular formal R- scheme X of pseudo- finite type, via the construction of a Gelfand- Leray form on its generic fiber. When X is the formal completion of a morphism f from a smooth irreducible variety to the affine line, then itsWeil generating series coincides (modulo normalization) with the motivic zeta function of f. When X is the formal completion of f at a closed point x of the special fiber f^{-1}(0), we obtain the local motivic zeta function of f at x.
ISSN: 0025-5831
Publication status: published
KU Leuven publication type: IT
Appears in Collections:Algebra Section
× corresponding author
# (joint) last author

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