Derived Algebraic Geometry Seminar: Formal geometry

Seminar | April 6 | 1-2 p.m. | 891 Evans Hall | Canceled

 Harrison Chen, UC Berkeley

 Department of Mathematics

Any map of prestacks has a good notion of formal completion via functor of points. A priori this formal completion may be difficult to study; we will discuss a method (due to Gaitsgory and Rozenblyum) by which one can write, in good cases, the formal completion of a colimit of infinitesimal neighborhoods. In the case of a closed embedding of good stacks, we recover the usual $n$th order thickenings. In the case of the map to a point, the formal completion is the de Rham stack, and the neighborhoods recover the (increasing) Hodge filtration of the dualizing sheaf.