STAGE Seminar

Featured Speaker:  Ishan Levy (MIT)

Title:  Infinitesimal site and algebraic de Rham cohomology

Abstract:  The de Rham cohomology of the analytification of a smooth projective variety over ℂ can be computed via an algebraic de Rham complex. Unfortunately, the algebraic de Rham complex is somewhat poorly behaved in positive characteristic. To solve this problem, Grothendieck showed first how to reinterpret de Rham cohomology in characteristic 0 as cohomology on a site (the infinitesimal site), and second how to modify the infinitesimal site to obtain a site that works well also in characteristic p (the crystalline site).

In this talk, we will explain algebraic de Rham cohomology and define the infinitesimal and stratifying sites. We also will define the notion of a classical Weil cohomology theory, which de Rham cohomology (char 0) and crystalline cohomology give examples of.

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