On the characteristic polynomial of the Frobenius on étale cohomology

Abstract

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 ${\mathbb{Q}}_l(d/2)$.

Revised version, several minor errors corrected

References in corpus (2)

• The Tate conjecture for K3 surfaces over finite fields
• On the computation of the Picard group for $K3$ surfaces

Cited by in corpus (3)

• K3 surfaces over finite fields with given L-function
• Eigenvalues and dynamical degrees of self-maps on abelian varieties
• Some non-special cubic fourfolds