Difference between revisions of "Algebra and Algebraic Geometry Seminar Spring 2018"
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Revision as of 11:10, 24 January 2018
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
|January 26||Tasos Moulinos (UIC)||Derived Azumaya Algebras and Twisted K-theory||Michael|
|February 2||Daniel Erman (Wisconsin)||TBA||Local|
|February 8 (unusual date!)||Roman Fedorov (University of Pittsburgh)||TBA||Dima|
|February 9||Juliette Bruce (Wisconsin)||TBA||Local|
|February 23||Aron Heleodoro (Northwestern)||TBA||Dima|
|April 6||Phil Tosteson (Michigan)||TBA||Steven|
|April 20||Alena Pirutka (NYU)||TBA||Jordan|
|April 27||Alexander Yom Din (Caltech)||TBA||Dima|
|May 4||John Lesieutre (UIC)||TBA||Daniel|
Derived Azumaya Algebras and Twisted K-theory
Topological K-theory of dg-categories is a localizing invariant of dg-categories over taking values in the -category of -modules. In this talk I describe a relative version of this construction; namely for a quasi-compact, quasi-separated -scheme I construct a functor valued in the -category of sheaves of spectra on , the complex points of . For inputs of the form where is an Azumaya algebra over , I characterize the values of this functor in terms of the twisted topological K-theory of . From this I deduce a certain decomposition, for a finite CW-complex equipped with a bundle of projective spaces over , of in terms of the twisted topological K-theory of ; this is a topological analogue of a result of Quillen’s on the algebraic K-theory of Severi-Brauer schemes.
Alexander Yom Din