A trace formula for F-crystals
type: Item
instance of: scholarly article
title: A trace formula for F-crystals
zbMATH Open document ID: 0539.14015
DOI: 10.1007/BF01388655
author: Anthony J. Scholl
published in: Inventiones Mathematicae
publication date: 1985-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/143184
review text: Let X be a smooth and proper curve over the finite field k, and let E be an F-crystal on X. In this paper the method of \textit{P. Monsky} [Ann. Math., II. Ser. 93, 315-343 (1971; Zbl 0213.475)] is adapted to prove a Lefschetz formula for the trace of F acting on the crystalline cohomology \(H^*(X/W,E)\), where W is the ring of Witt vectors of k, provided that char(k)\(\neq 2\). There is also discussion of a wider class of systems of coefficients for which the result is valid; namely, ''F-crystals with logarithmic singularities'', in which the underlying differential equation of E (on a smooth lifting of X to W) is permitted to have regular singular points.
Mathematics Subject Classification ID: 14F30
zbMATH DE Number: 3857277
zbMATH Keywords: F-crystal on proper curve
zbMATH Keywords: crystalline cohomology
zbMATH Keywords: F-crystals with logarithmic singularities
MaRDI profile type: Publication
cites work: \(p\)-adic cycles
cites work: Q3882554
cites work: Weak Formal Schemes
cites work: Formal cohomology. II: The cohomology sequence of a pair
cites work: Formal cohomology. III: Fixed point theorems
cites work: Formal cohomology. I
cites work: Modular forms and de Rham cohomology; Atkin-Swinnerton-Dyer congruences
OpenAlex ID: W1548966035
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description: scientific article; zbMATH DE number 3857277