Algebraic Geometry Seminar Spring 2018: Difference between revisions

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Topological K-theory of dg-categories is a localizing invariant of dg-categories over <math> \mathbb{C} </math>
Topological K-theory of dg-categories is a localizing invariant of dg-categories over <math> \mathbb{C} </math>
taking values in the infinity category of KU-modules. In this talk I describe a relative version
taking values in the infinity category of <math> KU </math>-modules. In this talk I describe a relative version
of this construction; namely for X a quasi-compact, quasi-separated C-scheme I construct a
of this construction; namely for X a quasi-compact, quasi-separated C-scheme I construct a
functor valued in the infinity category of sheaves of spectra on X(C), the complex points of X. For inputs
functor valued in the infinity category of sheaves of spectra on X(C), the complex points of X. For inputs

Revision as of 12:53, 17 January 2018

The seminar meets on Fridays at 2:25 pm in room B113.

Here is the schedule for the previous semester.

Algebraic Geometry Mailing List

  • Please join the AGS Mailing List to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).

Spring 2018 Schedule

date speaker title host(s)
January 26 Tasos Moulinos (UIC) TBA Michael
February 23 Aron Heleodoro (Northwestern) TBA Dima
March 9 Phil Tosteson (Michigan) TBA Steven
April 20 Alena Pirutka (NYU) TBA Jordan
April 27 Alexander Yom Din (Caltech) TBA Dima

Abstracts

Tasos Moulinos

Derived Azumaya Algebrais and Twisted K-theory

Topological K-theory of dg-categories is a localizing invariant of dg-categories over [math]\displaystyle{ \mathbb{C} }[/math] taking values in the infinity category of [math]\displaystyle{ KU }[/math]-modules. In this talk I describe a relative version of this construction; namely for X a quasi-compact, quasi-separated C-scheme I construct a functor valued in the infinity category of sheaves of spectra on X(C), the complex points of X. For inputs of the form Perf(X, A) where A is an Azumaya algebra over X, I characterize the values of this functor in terms of the twisted topological K-theory of X(C). From this I deduce a certain decomposition, for X a finite CW-complex equipped with a bundle P of projective spaces over X, of KU(P) in terms of the twisted topological K-theory of X ; this is a topological analogue of a result of Quillen’s on the algebraic K-theory of Severi-Brauer schemes.

Aron Heleodoro

TBA

Alexander Yom Din

TBA