David Kern: Derived infinitesimal foliations, after Toën–Vezzosi (contd.)

Abstract:

I will describe the constructions and results of the paper arXiv:2305.13010  by Toën–Vezzosi defining derived infinitesimal foliations, a variant of their earlier derived foliations in positive characteristic, that unlike the latter are always formally integrable, and relate to infinitesimal cohomology rather than de Rham or crystalline cohomology. The construction will take us through the world of graded circles in order to capture the algebraic structures of mixed differentials, and use ideas of non-connective derived geometry so as to compare the different shifts between the two kinds of foliations.