Date: Wednesday, May 25, 2022
Location: 2866 East Hall (2:00 PM to 4:00 PM)
Title: G aperfmules and de Rham cohomology
Abstract: In this thesis, we prove that algebraic de Rham cohomology as a functor defined on smooth F_palgebras is formally \'etale in a precise sense. This result shows that given de Rham cohomology, one automatically obtains the theory of crystalline cohomology as its \textit{unique} functorial deformation. To prove this, we define and study the notion of a pointed {G}_a^{perf}module and its refinement which we call a quasiideal in {G}_a^{perf}  following Drinfeld's terminology. Our main constructions show that there is a way to ``unwind" any pointed {G}_a^{perf}module and define a notion of a cohomology theory for algebraic varieties. We use this machine to redefine de Rham cohomology theory and deduce its formal \'etalness and a few other properties.
Shubhodip's advisor is Bhargav Bhatt.
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Speaker: Shubhodip Mondal
Institution: UM
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