### NICK ROZENBLYUM THESIS

A key player in the story is the deRham stack, introduced by Simpson in the context of nonabelian Hodge theory. This immediately implies the statement for any finite extension of K. Mon, 22 Oct Sun, 4 Nov Department Massachusetts Institute of Technology.

The scientific name for this is “Weil restriction of scalars”. Thu, 11 Oct JavaScript is disabled for your browser. Publisher Massachusetts Institute of Technology. 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. 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.

## Motives and derived algebraic geometry

One uses here the following fact: 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. Sun, rozdnblyum Sep So we have plenty of time to think rozenvlyum Nick’s talks! Thursday October 184: 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 of unipotent groups over finite fields.

Mon, 29 Oct We describe this category in terms of the action of infinitesimal Hecke functors on the category of quasi-coherent sheaves on Bung. Sarnak’s second Albert lecture is at 3 p. Categories of D-modules on spaces of rational maps arise in the context of the geometric Langlands program. thssis

# David Ayala – David Ayala | Montana State University

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. October 4 Thursday and October 8 Monday. All the necessary background will be provided. 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.

Publisher Massachusetts Institute of Technology. I will explain how each of the different models for these spaces exhibit different properties of their categories of D-modules. Abstract I will discuss the equivalence between three different models for spaces of rational maps in algebraic geometry. Models for spaces of rational maps. 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.

Models for spaces of rational maps Abstract I will discuss the equivalence between three different models for spaces of rational maps in algebraic geometry.

We show that sheaves which are, in a certain sense, equivariant with respect to infinitesimal Hecke functors are exactly D-modules, i.

This construction has a number of benefits; for instance, Kashiwara’s Lemma and h-descent are easy consequences of the definition. The latter will be devoted to a new approach to the foundations of D-module theory developed by Gaitsgory and Rozenblyum.

A key player in the story is the deRham stack, introduced by Simpson in the context of nonabelian Hodge theory.

Department Massachusetts Institute of Technology. Wed, 7 Nov Thu, 8 Nov Other Contributors Massachusetts Institute of Technology. Download Full printable version 3. I will begin with an overview of Grothendieck-Serre duality in derived algebraic geometry via the formalism of ind-coherent sheaves.

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## Nick rozenblyum thesis –

Crystals, D-modules, and derived algebraic geometry. Wed, 17 Oct This gives a description of flat connections on a quasi-coherent sheaf on Bung which is local on the Ran space.

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.