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# Documents  14D23 | enregistrements trouvés : 6

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## Stacks and categories in geometry, topology, and algebra.CATS4 conference on higher categorical structures and their interactions with algebraic geometry, algebraic topology and algebraMarseille # July 2-7, 2012 Pantev, Tony ; Simpson, Carlos ; Toën, Bertrand ; Vaquie, Michel ; Vezzosi, Gabriele | American Mathematical Society 2015

Congrès

- viii; 323 p.
ISBN 978-1-4704-1557-0

Contemporary mathematics , 0643

Localisation : Collection 1er étage

préfaisceau algébrique # topologie algébrique # géométrie algébrique # théorie des catégories # faisceau

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## Development of moduli theory - Kyoto 2013.Proceedings of the 6th Mathematical Society of Japan-Seasonal Institute, MSJ-SIKyoto # June 11-21, 2013 Fujino, Osamu ; Kondo, Shigeyuki ; Moriwaki, Atsushi ; Saito, Masa-Hico ; Yoshioka, Kota | Mathematical Society of Japan 2016

Congrès

- 537 p.
ISBN 978-4-86497-032-7

Advanced studies in pure mathematics , 0069

Localisation : Collection 1er étage

théorie des modules # géométrie algébrique

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## Character stacks and $(q-)$geometric representation theory Gunningham, Sam | CIRM H

Multi angle

Research talks

I will discuss applications of geometric representation theory to topological and quantum invariants of character stacks. In particular, I will explain how generalized Springer correspondence for class $D$-modules and Koszul duality for Hecke categories encode surprising structure underlying the homology of character stacks of surfaces (joint work with David Ben-Zvi and David Nadler). I will then report on some work in progress with David Jordan and Pavel Safronov concerning a q-analogue of these ideas. The applications include an approach towards Witten’s conjecture on the fi dimensionality of skein modules, and methods for computing these dimensions in certain cases. I will discuss applications of geometric representation theory to topological and quantum invariants of character stacks. In particular, I will explain how generalized Springer correspondence for class $D$-modules and Koszul duality for Hecke categories encode surprising structure underlying the homology of character stacks of surfaces (joint work with David Ben-Zvi and David Nadler). I will then report on some work in progress with David Jordan ...

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## ​On the motive of the stack of vector bundles on a curve Hoskins, Victoria | CIRM H

Multi angle

Research talks;Algebraic and Complex Geometry

Following Grothendieck’s vision that a motive of an algebraic variety should capture many of its cohomological invariants, Voevodsky introduced a triangulated category of motives which partially realises this idea. After describing some of the properties of this category, I explain how to define the motive of certain algebraic stacks. I will then focus on defining and studying the motive of the moduli stack of vector bundles on a smooth projective curve and show that this motive can be described in terms of the motive of this curve and its symmetric powers. If there is time, I will give a conjectural formula for this motive, and explain how this follows from a conjecture on the intersection theory of certain Quot schemes. This is joint work with Simon Pepin Lehalleur. Following Grothendieck’s vision that a motive of an algebraic variety should capture many of its cohomological invariants, Voevodsky introduced a triangulated category of motives which partially realises this idea. After describing some of the properties of this category, I explain how to define the motive of certain algebraic stacks. I will then focus on defining and studying the motive of the moduli stack of vector bundles on a smooth ...

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## Tannaka duality and formal glueings Hall, Jack | CIRM H

Multi angle

Research talks;Algebraic and Complex Geometry

After recalling classical Tannaka duality for finite groups, I will discuss an extension to equivariant algebraic geometry, and more generally to algebraic stacks. Surprisingly, this is related to formal glueings and Neron-Popescu desingularization.

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## Algebraic spaces and stacks Olsson, Martin | American Mathematical Society 2016

Ouvrage

- xi; 298 p.
ISBN 978-1-4704-2798-6

American mathematical society colloquium publications , 0062

Localisation : Collection 1er étage

géométrie algébrique # espace algébrique # empilement algébrique # fibration # espace de modules fins # espace de modules grossiers

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