## NICK ROZENBLYUM THESIS

Wed, 17 Oct Models for spaces of rational maps. Crystals, D-modules, and derived algebraic geometry. Models for spaces of rational maps Abstract I will discuss the equivalence between three different models for spaces of rational maps in algebraic geometry. I will explain its construction and basic properties. Thu, 11 Oct

Thu, 15 Nov Gaitsgory formulating the theory of D-modules using derived algebraic geometry. Metadata Show full item record. I will begin with an overview of Grothendieck-Serre duality in derived algebraic geometry via the formalism of ind-coherent sheaves. 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 Kashiwara , and some basic ideas of the Gaitsgory-Rosenblum theory. I will explain how each of the different models for these spaces exhibit different properties of their categories of D-modules.

Mon, 29 Oct Terms of use M.

Sun, 30 Sep Mon, 12 Nov This immediately implies the statement for any finite extension of K. I will explain its construction and basic properties.

Models for spaces of rational maps. Duality and D-modules via derived algebraic geometry. The scientific name for this is “Weil restriction of scalars”. Thursday October 184: All the necessary background will be provided.

## David Ayala

Mon, 24 Sep Connections on conformal blocks Author s Rozenblyum, Nikita. Part of the talk will be based on joint work with Jared Weinstein Boston University.

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.

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

# Motives and derived algebraic geometry – Essen, May

It is a convenient formulation of Gorthendieck’s theory of crystals in characteristic 0. Wed, 7 Nov Nick will continue next Thursday: Beilinson’s talk is intended thsis be a kind of introduction to those by Rozenblyum.

I make there two additional assumptions, which are not really necessary: 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. A key player in the story is the deRham stack, introduced by Simpson in dozenblyum context of nonabelian Hodge theory.

On Nov nock Monday Jonathan Barlev will begin his series of talks on the spaces of rational maps. We describe this category in terms of the action of infinitesimal Hecke functors on the category of quasi-coherent sheaves on Bung. I will also explain how this approach compares to more familiar definitions.

# Nick rozenblyum thesis

Some features of this site may not work without it. The latter will be devoted to a new approach to tesis foundations of D-module theory developed by Gaitsgory and Rozenblyum.

JavaScript is disabled for your browser. 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

Collections Mathematics – Ph. 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.

D-modules in infinite type. This gives a description of flat connections on a quasi-coherent sheaf on Bung which is local on the Ran space. Department Massachusetts Nickk of Technology.