Topological Hochschild cohomology for schemes

Abstract: Topological Hochschild cohomology is a sort of refinement of usual Hochschild cohomology that incorporates data from stable homotopy theory. Instead of working over a base ring, one works over the sphere spectrum, which is a commutative ring in an appropriate sense. I'll give a quick introduction to spectral algebra and THH^*. Then I'll define the THH^* of a scheme in a `derived noncommutative' way - i.e. using appropriate dg categories of sheaves - and explain some invariance results, which in the non-topological setting are due to Lowen and Van den Bergh via Keller. I'll discuss some toy non-affine computations, and time permitting I'll talk about the relationship to deformation theory, especially in positive characteristic. This is joint work with Dmitry Kaledin and Wendy Lowen.

mathematical physicscommutative algebraalgebraic geometryrings and algebrasrepresentation theorysymplectic geometry

Audience: researchers in the topic

( slides | video )

Comments: https://us02web.zoom.us/j/87160036709 Meeting ID: 871 6003 6709 Passcode: LAGOON

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Longitudinal Algebra and Geometry Open ONline Seminar (LAGOON)

Series comments: Description: Research webinar series

The LAGOON webinar series was supported as part of the International Centre for Mathematical Sciences (ICMS) and the Isaac Newton Institute for Mathematical Sciences (INI) Online Mathematical Sciences Seminars and is now sponsored by the University of Cologne and the University of Pavia. Please register here to obtain the Zoom link and password for the meetings.

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