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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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 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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ispartof Duke mathematical journal, 2015-08, Vol.164 (11), p.2161-2184
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1547-7398
language eng
recordid cdi_projecteuclid_primary_oai_CULeuclid_euclid_dmj_1439470581
source Project Euclid
subjects 14F20
14G15
14J20
14J35
Artin-Tate formula
Characteristic polynomial
Frobenius
Middle cohomology
Proper variety over finite field
title On the characteristic polynomial of the Frobenius on étale cohomology
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