Algebraic Geometry Seminar Spring 2018

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

Here is the schedule for the previous semester.

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Spring 2018 Schedule

date speaker title host(s)
January 26 Tasos Moulinos (UIC) TBA Michael
February 23 Aron Heleodoro (Northwestern) TBA Dima
April 6 Phil Tosteson (Michigan) TBA Steven
April 13 Reserved Daniel
April 20 Alena Pirutka (NYU) TBA Jordan
April 27 Alexander Yom Din (Caltech) TBA Dima


Tasos Moulinos

Derived Azumaya Algebras and Twisted K-theory

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


Alexander Yom Din