On the characteristic polynomial of the Frobenius on étale cohomology

Let X be a smooth proper variety of even dimension d over a finite field. We establish a restriction on the value at (-1) of the characteristic polynomial of the Frobenius on the middle-dimensional étale cohomology of X with coefficients in { \mathbb{Q}}_{l}(d/2) .

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Bibliographic Details
Published in:Duke mathematical journal 2015-08, Vol.164 (11), p.2161-2184
Main Authors: Elsenhans, Andreas-Stephan, Jahnel, Jörg
Format: Article
Language:English
Subjects:
14F20
14G15
14J20
14J35
Artin-Tate formula
Characteristic polynomial
Frobenius
Middle cohomology
Proper variety over finite field
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Description
Summary:Let X be a smooth proper variety of even dimension d over a finite field. We establish a restriction on the value at (-1) of the characteristic polynomial of the Frobenius on the middle-dimensional étale cohomology of X with coefficients in { \mathbb{Q}}_{l}(d/2) .
ISSN:0012-7094
1547-7398
DOI:10.1215/00127094-3129381