### NICK ROZENBLYUM THESIS

D-modules in infinite type. I will begin with an overview of Grothendieck-Serre duality in derived algebraic geometry via the formalism of ind-coherent sheaves. Mon, 12 Nov Department Massachusetts Institute of Technology. Terms of use M.

Publisher Massachusetts Institute of Technology. Other Contributors Massachusetts Institute of Technology. Download Full printable version 3. Thu, 8 Nov The category of D-modules is defined as sheaves in the deRham stack.

I will explain how each of the different models for these spaces exhibit different properties of their categories of D-modules. Department Massachusetts Institute of Technology. Models for spaces of thesls maps. It is a convenient formulation of Gorthendieck’s theory of crystals in characteristic 0.

# Motives and derived algebraic geometry – Essen, May

They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. Wed, 17 Oct Mon, 29 Oct 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.

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

I will discuss the notion of crystals and de Rham coefficients that goes back to Rozebblyum, the derived D-module functoriality for smooth varieties due to Bernstein and Kashiwaraand some basic ideas of the Gaitsgory-Rosenblum theory. Crystals, D-modules, and derived algebraic geometry. October 4 Thursday and October 8 Monday. So we have plenty of time to think about Nick’s talks!

This immediately implies the statement for any finite extension of K.

# Nick rozenblyum thesis

Mon, 22 Oct Terms of use M. Thu, 4 Oct Sun, 4 Nov I will also explain how this approach compares to more familiar definitions. 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. The scientific name for this is “Weil restriction of scalars”. Thu, 15 Nov We describe this category in terms of the action of infinitesimal Hecke functors on the category of quasi-coherent sheaves on Bung.

## Motives and derived algebraic geometry

Beilinson’s talk is intended to be a kind of introduction to those by Rozenblyum. An analysis of Lusztig’s construction and of the Lubin-Tate tower of K leads to interesting new varieties that provide an analogue of Deligne-Lusztig theory for certain families rozehblyum unipotent groups over finite fields.

I will explain its construction and basic properties. I make there two additional assumptions, which are not really necessary: Mon, 24 Sep The latter will be devoted to a new approach to the foundations of D-module theory thesls by Gaitsgory and Rozenblyum. Other Contributors Massachusetts Institute of Technology.

Mon, 8 Oct Wed, 7 Nov Download Full printable version 3. 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. Sun, 30 Sep Connections on conformal blocks Author s Rozennlyum, Nikita.