Abstract:
Cohomological descent was invented by Deligne in the early 60's. I recall memories about this and discuss related developments and applications that arose since then, pertaining to cotangent complex and deformation theory, mixed Hodge theory, de Jong alterations, $p$-adic Hodge theory.
Key words and phrases:Galois descent, cohomological descent, hypercovering, simplicial space, Grothendieck's six operations, cotangent complex, first order deformation, algebraic stack, mixed Hodge theory, de Jong alteration, rigid cohomology, $p$-adic étale cohomology, $p$-adic Hodge theory, independence of $\ell$.
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