Algebraic Geometry Seminar

Please see the following for more related talks:

• geometry/topology seminar
• string theory seminar

• Wednesday, December 6, 2023, 1:30pm, Gross Hall 304B, Algebraic Geometry Seminar
  Prismatic F-gauges and Fontaine-Laffaille modules
  Vadim Vologodsky

   

  The category of prismatic F-gauges on a p-adic scheme X, recently introduced by Bhatt-Lurie and Drinfeld, plays a role similar to the category of Hodge D-modules attached to a variety over the field of complex numbers. It is the input to classifications of geometric objects over X such as p-divisible groups as well as computations in algebraic K-theory. It is also a tool for describing Galois representations associated with schemes over p-adic fields. The category of prismatic F-gauges is very interesting already for X being the spectrum of p-adic integers: the prismatic F-gauge associated to a scheme Y over Z_p remembers the information about prismatic cohomology of Y associated with any prism. In the first part of my talk I review the notion of prismatic F-gauge. Then I will explain how a full subcategory of the category of prismatic F-gauges formed by objects whose Hodge-Tate weights lie in the interval [0,p-2] is equivalent to the derived category of Fontaine-Laffaille modules with a similar weight constrain. In the geometric context, this means that the prismatic F-gauge associated with a formally smooth scheme over p-adic integers of dimension < p-1 can be recovered from its Hodge filtered de Rham cohomology equipped with the Nygaard refined crystalline Frobenius endomorphism. If time permits I will explain a generalization of the above statement to the case of prismatic F-gauges over a smooth p-adic formal scheme. The talk is based on a joint work with Gleb Terentiuk and Yujie Xu.

• Wednesday, January 10, 2024, 1:30pm, Zoom link, Algebraic Geometry Seminar
  TBA
  Alberto San Miguel Malaney (U Texas at Austin, Mathematics)

• Wednesday, February 14, 2024, 1:30pm, Zoom link, Algebraic Geometry Seminar
  TBA
  Daniel Greb (Universität Duisburg-Essen)

• Wednesday, March 27, 2024, 1:30pm, Zoom link, Algebraic Geometry Seminar
  TBA
  David Urbanik (IHES)