Duke Mathematical Journal

On the characteristic polynomial of the Frobenius on étale cohomology

Andreas-Stephan Elsenhans and Jörg Jahnel

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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 Ql(d/2).

Article information

Duke Math. J., Volume 164, Number 11 (2015), 2161-2184.

Received: 27 November 2013
Revised: 11 September 2014
First available in Project Euclid: 13 August 2015

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Zentralblatt MATH identifier

Primary: 14F20: Étale and other Grothendieck topologies and (co)homologies
Secondary: 14G15: Finite ground fields 14J20: Arithmetic ground fields [See also 11Dxx, 11G25, 11G35, 14Gxx] 14J35: $4$-folds

Proper variety over finite field Middle cohomology Frobenius Characteristic polynomial Artin-Tate formula


Elsenhans, Andreas-Stephan; Jahnel, Jörg. On the characteristic polynomial of the Frobenius on étale cohomology. Duke Math. J. 164 (2015), no. 11, 2161--2184. doi:10.1215/00127094-3129381. https://projecteuclid.org/euclid.dmj/1439470581

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