Japanese Journal of Mathematics

, Volume 1, Issue 1, pp 107–136

Miscellany on traces in ℓ-adic cohomology: a survey


DOI: 10.1007/s11537-006-0504-3

Cite this article as:
Illusie, L. Jpn. J. Math. (2006) 1: 107. doi:10.1007/s11537-006-0504-3


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

Keywords and phrases.

ℓ-adic cohomology independence of ℓ Grothendieck’s trace formula Lefschetz trace formula zeta functions over finite fields Euler–Poincaré characteristic Betti number Bloch’s conductor conjecture intersection cohomology Grothendieck’s six operations intermediate extension Weil conjectures Hodge polygon Newton polygon crystalline cohomology Hodge filtration coniveau filtration alteration Fano variety rationally connected Weil group Swan conductor wild ramification Brauer trace log scheme logarithmic differential forms Čebotarev’s density theorem semisimple group Fatou’s lemma 

Mathematics Subject Classification (2000).

14F20 (primary) 14F10 20G15 (secondary) 

Copyright information

© The Mathematical Society of Japan and Springer-Verlag 2006

Authors and Affiliations

  1. 1.Département de MathématiqueUniversité de Paris-SudOrsay CedexFrance

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