Constraints on the cohomological correspondence associated to a self map

TL;DR

This paper investigates restrictions on the eigenvalues of a self map acting on the $ ext{l}$-adic cohomology of a proper variety, utilizing a trace formula and weight theory to derive these constraints.

Contribution

It introduces new constraints on eigenvalues of self maps on cohomology, combining trace formulas with weight theory in algebraic geometry.

Findings

Eigenvalues are subject to specific bounds and restrictions.

Trace formula and weight theory provide effective tools for analysis.

Results apply to proper varieties in algebraic geometry.

Abstract

In this article we establish some constraints on the eigenvalues for the action of a self map of a proper variety on its $\ell$-adic cohomology. The essential ingredients are a trace formula due to Fujiwara, and the theory of weights.