### NICK ROZENBLYUM THESIS

Thu, 18 Oct The category of D-modules is defined as sheaves in the deRham stack. D-modules in infinite type. Models for spaces of rational maps Abstract I will discuss the equivalence between three different models for spaces of rational maps in algebraic geometry. See provided URL for inquiries about permission. This family of functors, parametrized by the Ran space of X, acts by averaging a quasi-coherent sheaf over infinitesimal modifications of G-bundles at prescribed points of X. Categories of D-modules on spaces of rational maps arise in the context of the geometric Langlands program.

Models for spaces of rational maps. Duality and D-modules via derived algebraic geometry. Mon, 24 Sep On Nov 12 Monday Jonathan Barlev will begin his series of talks on the spaces of rational maps. This family of functors, parametrized by the Ran space of X, acts by averaging a quasi-coherent sheaf over infinitesimal modifications of G-bundles at prescribed points of X. Gaitsgory formulating the theory of D-modules using derived algebraic geometry.

This gives a description of flat connections on a quasi-coherent sheaf on Bung which is local on the Ran space.

## Motives and derived algebraic geometry

Publisher Massachusetts Institute of Technology. Download Full printable version 3.

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.

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.

October 4 Thursday and October 8 Monday. It is a convenient formulation of Gorthendieck’s theory of crystals in characteristic 0. This is an archive of email messages concerning the Geometric Langlands Seminar for In particular, I will explain the relation between spaces of quasi-maps and the model for the space of rational maps which Gaitsgory uses in his recent contractibility theorem.

Thursday October 184: D-modules in infinite type.

# Nick rozenblyum thesis

This construction has a nicck of benefits; for instance, Kashiwara’s Lemma and h-descent are easy consequences of the definition. Department Massachusetts Institute of Technology.

Sun, 30 Sep I make there two additional assumptions, which are not really necessary: Wed, 17 Oct Rozehblyum provided URL for inquiries about permission. The scientific name for this is “Weil restriction of scalars”. Connections on conformal blocks Author s Rozenblyum, Nikita.

Metadata Show full item record. The theory of D-modules will be built as an extension of this theory. An analysis of Lusztig’s construction and rozneblyum the Lubin-Tate tower of K leads to interesting new varieties that provide an analogue of Deligne-Lusztig theory for certain families of unipotent groups over finite fields.

I will describe the known examples of this phenomenon and their relationship to the local Langlands correspondence. Duality and D-modules via derived algebraic geometry. On Nov 12 Monday Jonathan Barlev will begin his series of talks on the spaces of rational maps. I will explain how each of the nuck models for these spaces exhibit different properties of their categories of D-modules.

We show that sheaves which are, in a certain sense, equivariant with respect to infinitesimal Hecke functors are exactly D-modules, i. I will explain its construction and basic properties. Abstract I will describe joint work with D. The latter will be devoted to a new approach to the foundations of D-module theory developed by Gaitsgory and Rozenblyum.

Mon, 8 Oct Mon, 24 Sep Thu, 18 Oct They may be thesi from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission.

# Connections on conformal blocks

This implies the statement in the more general setting considered at the seminar when the target variety is connected and locally isomorphic to an affine space. All the necessary background will be provided.

Crystals, D-modules, and derived algebraic geometry.