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# Dissertation Defense Seminar

G a-perf-mules and de Rham cohomology
Wednesday, May 25, 2022
2:00-4:00 PM
2866 East Hall Map
In this thesis, we prove that algebraic de Rham cohomology as a functor defined on smooth F_p-algebras 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 quasi-ideal 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. Speaker(s): Shubhodip Mondal (UM)
Building: East Hall Workshop / Seminar Mathematics Happening @ Michigan from Department of Mathematics