Japan. J. Math. 1, 107--136 (2006)

Miscellany on traces in $\ell$-adic cohomology : a survey

Luc Illusie

Abstract: We discuss classical questions concerning traces of elements of Galois groups or correspondences in $\ell$-adic cohomology, mostly over finite or local fields, such as rationality and independence of $\ell$, integrality, congruences modulo powers of $\ell$ or $p$. We report on the progress that has been made on this topic during the past ten years.