Algebraic Geometry Seminar Spring 2018: Difference between revisions
| Line 51: | Line 51: | ||
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