Categories of D-modules on spaces of rational maps arise in the context of the geometric Langlands program. I will explain how each of the different models for these spaces exhibit different properties of their categories of D-modules. Gaitsgory formulating the theory of D-modules using derived algebraic geometry. Duality and D-modules via derived algebraic geometry. We show that sheaves which are, in a certain sense, equivariant with respect to infinitesimal Hecke functors are exactly D-modules, i. Other Contributors Massachusetts Institute of Technology.
Collections Mathematics – Ph. Thu, 18 Oct I will describe the known examples of this phenomenon and their relationship to the local Langlands correspondence. Thesus 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 explain its construction and basic properties. Thu, 15 Nov This immediately implies the statement for any finite extension of K.
Nick rozenblyum thesis
It is a convenient formulation of Gorthendieck’s theory of crystals in characteristic 0. We describe this category in terms of the action of infinitesimal Hecke functors on the category of quasi-coherent sheaves on Bung.
Other Contributors Massachusetts Institute of Technology. Connections on conformal blocks Author s Rozenblyum, Nikita.
Download Full printable version 3. 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. Mon, 22 Oct Publisher Massachusetts Institute of Technology. One uses here the following fact: Rozenhlyum 4 Thursday and October 8 Monday.
Motives and derived algebraic geometry – Essen, May
Sun, 4 Nov Mon, 12 Nov 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 rozenbljum of the Gaitsgory-Rosenblum theory. Wed, 7 Nov Thu, 8 Nov A key player in the story is the deRham stack, introduced by Simpson in the context of nonabelian Hodge theory.
Mon, 29 Oct This gives a description of flat connections on a quasi-coherent sheaf on Bung which is local on the Ran space.
Metadata Show full item record. I will explain how each of the different models for these spaces rozenbluym different properties of their categories of D-modules.
Sarnak’s second Albert lecture is at 3 p. Abstract I will discuss the equivalence between three different models for spaces of rational maps in algebraic geometry. Abstract This is an introduction to a series of talks of Nick Rosenblum on his foundational work with Dennis Gaitsgory that establishes the basic D-module functoriality in the context of derived algebraic geometry hence for arbitrary singular algebraic varieties over a field of characteristic 0.
Beilinson’s talk is intended to be a kind of introduction to those by Rozenblyum.
Motives and derived algebraic geometry
The scientific name for this is “Weil restriction of scalars”. 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. Crystals, D-modules, and derived algebraic geometry.