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Miscellany on traces in \(\ell\)-adic cohomology: a survey. (English) Zbl 1156.14309

Summary: 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.

MSC:

14F20 Étale and other Grothendieck topologies and (co)homologies
14F10 Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials
20G15 Linear algebraic groups over arbitrary fields
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