### NICK ROZENBLYUM THESIS

Thu, 15 Nov See provided URL for inquiries about permission. Wed, 7 Nov Other Contributors Massachusetts Institute of Technology. Already in Lusztig proposed a very elegant, but still conjectural, geometric construction of twisted parabolic induction for unramified maximal tori in arbitrary reductive p-adic groups. Department Massachusetts Institute of Technology. Thu, 11 Oct

Models for spaces of rational maps. All the necessary background will be provided. Part of the talk will be based on joint work with Jared Weinstein Boston University. I make there two additional assumptions, which are not really necessary: Publisher Massachusetts Institute of Technology.

## David Ayala

Part of the talk will be based on joint work with Jared Weinstein Boston University. See provided URL for inquiries about permission. I will explain its construction and basic properties. Crystals, D-modules, and derived algebraic geometry.

Nick will continue next Thursday: The scientific name for this is “Weil restriction of scalars”. Sarnak’s second Albert lecture is at 3 p. One uses here the following fact: I will describe the known examples of this phenomenon and their relationship to the local Langlands correspondence.

# Motives and derived algebraic geometry – Essen, May

Mon, 22 Oct Terms of use M. Abstract I will describe joint work with D. Thu, 18 Oct So we have plenty of time to think about Nick’s talks!

The theory of D-modules will be built as an extension of this theory. Publisher Massachusetts Institute of Technology.

I will begin with an overview of Grothendieck-Serre duality in derived algebraic geometry via the formalism of ind-coherent sheaves. In particular, I will explain the relation between spaces of quasi-maps and the model for the tthesis of rational maps which Gaitsgory uses in his recent contractibility theorem. Models for spaces of rational maps.

Mon, 29 Oct Thu, 15 Nov However, as such spaces are not representable by ind- schemes, the construction of such categories relies on the general theory presented in Nick Rozenblyum’s talks. Thu, 11 Oct Categories of D-modules on spaces of rational maps arise in the context of the geometric Langlands program.

Mon, 24 Sep I make there two additional assumptions, which inck not really necessary: Abstract I will discuss the equivalence between three different models for spaces of rational maps in algebraic geometry. Beilinson’s talk is intended to theais a kind of introduction to those by Rozenblyum.

I will discuss the notion of crystals and de Rham coefficients that goes back to Grothendieck, the derived D-module functoriality for smooth varieties due to Bernstein and Kashiwaraand some basic ideas of the Gaitsgory-Rosenblum theory.

I will also explain how this approach compares to more familiar definitions.

# David Ayala – David Ayala | Montana State University

I will explain how each of the different models for these spaces exhibit different properties of their categories of D-modules. Already in Lusztig proposed a very elegant, but still conjectural, geometric construction of twisted parabolic induction for unramified maximal tori in arbitrary reductive p-adic groups.

We describe this category in terms of the action of infinitesimal Hecke functors on the category of quasi-coherent sheaves on Bung. Metadata Show full item record. Gaitsgory formulating the theory of D-modules using derived algebraic geometry.