Beilinson’s talk is intended to be a kind of introduction to those by Rozenblyum. Models for spaces of rational maps Abstract I will discuss the equivalence between three different models for spaces of rational maps in algebraic geometry. This immediately implies the statement for any finite extension of K. I will explain its construction and basic properties. A key player in the story is the deRham stack, introduced by Simpson in the context of nonabelian Hodge theory. I will also explain how this approach compares to more familiar definitions. No previous knowledge of the above subjects is needed.

October 4 Thursday and October 8 Monday. I will begin with an overview of Grothendieck-Serre duality in derived algebraic geometry via the formalism of ind-coherent sheaves. Wed, 7 Nov D-modules in infinite type. Other Contributors Massachusetts Institute of Technology.

## Nick rozenblyum thesis –

The latter will be devoted to a new approach to the foundations of D-module theory developed by Gaitsgory and Rozenblyum. It is a convenient formulation of Gorthendieck’s theory of crystals in characteristic 0.

Models for spaces of rational maps. The scientific name for this is “Weil restriction of scalars”. 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. October 4 Thursday rpzenblyum October 8 Monday. Thu, 8 Nov 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.

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. Department Massachusetts Institute of Technology.

# Motives and derived algebraic geometry – Essen, May

This gives a description of flat connections on a quasi-coherent sheaf on Bung which is local on the Ran space. Abstract For an algebraic group G and a projective curve X, we study the category of D-modules on the moduli space Bung of principal G-bundles on X using ideas from conformal field theory.

Gaitsgory formulating the theory of D-modules using derived algebraic geometry. Thu, 4 Oct This construction has a number of benefits; for instance, Kashiwara’s Lemma and h-descent are easy consequences of the definition. Thu, 18 Oct D-modules in infinite type. Thu, 15 Nov They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. One uses here the following fact: Collections Mathematics – Ph. Sun, 30 Sep Mon, 22 Oct This immediately implies the statement for any finite extension of K.

## Motives and derived algebraic geometry

Thu, 11 Oct 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.

We describe this category in terms of the action of infinitesimal Hecke functors on the category of quasi-coherent sheaves on Bung. Mon, 29 Oct Nick will continue next Thursday: Part of the talk will be based on joint work with Jared Weinstein Boston University.

I will explain how each of the different models for these spaces exhibit different properties of their categories of D-modules.

Sarnak’s second Albert lecture is at 3 p. Metadata Show full item record.

Terms of use M. 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 yhesis of X.

Mon, 12 Nov