A topological point of view for the Galois action on étale Cohomology.

par François Gatine (IMJ-PRG, Sorbonne Université)

mercredi 18 févr. 2026, 14:00 → 15:15 Europe/Paris

Salle Pierre Grisvard (IHP - Bâtiment Borel)

In the study of nice enough topological spaces, algebraic topology introduces singular cohomology groups; these are objects of linear algebraic nature which can be linked to numerous properties of spaces. When studying families of spaces, one can package the cohomology of all spaces into a single object: a local system.
For algebraic varieties, the naive definition of singular cohomology breaks down. The proper replacement is étale (more specifically, \ell-adic) cohomology, which is notoriously technical to define. It is common knowledge that these cohomology groups come equipped with a mysterious Galois action, the origin of which can be swept under the rug by invoking "functoriality". In this talk, I expand on a point of view in which the definition of étale cohomology exactly parallels that of singular cohomology. The Galois action then naturally appears as a necessity from the theory of étale local systems.