Beyond crystalline cohomology, rigid cohomology

par Thomas Serafini (DMA)

mercredi 4 nov. 2026, 15:30 → 16:30 Europe/Paris

Pierre Grisvard (IHP)

Crystalline cohomology is not a "good" cohomology for non-proper varieties - for instance, the crystalline H¹ of the affine line is not finite-dimensional. Following ideas from Monsky and Washnitzer, Berthelot defined rigid cohomology on general varieties in characteristic p > 0, which provides the "right" extension of crystalline cohomology to arbitrary varieties. The central idea is that of overconvergence, i.e. considering analytic functions that converge not on a p-adic lifting of the variety, but rather on a neighborhood of it. Following and detailing the example of the affine line, we will build to the definition of rigid cohomology and explain its relation to p-adic differential equations.