EVENT DETAILS AND ABSTRACT

Title: Noncommutative crystalline complex and the Gauss Manin connection
Speaker: Boris Tsygan
Speaker Info: Northwestern
Brief Description:
Special Note:
Abstract:

For an algebra over a finite field we construct a complex of modules over the Witt vectors. When the algebra admits a lifting to an algebra of Witt vectors, this complex is the completed periodic cyclic complex of the lifting (in particular, the complex does not depend on a lifting, in a strong sense that we will specify). This work is closely related to recent works of Petrov, Vayntrob, and Vologodsky. The construction follows from the same algebraic structure on cyclic complexes as a refined version of Getzler’s Gauss Manin connection.