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.