Algebraic Geometry Seminar Spring 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
| date | speaker | title | host(s) |
|---|---|---|---|
| January 26 | Tasos Moulinos (UIC) | Derived Azumaya Algebras and Twisted K-theory | Michael |
| February 2 | Daniel Erman (Wisconsin) | TBA | Local |
| 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 |
Abstracts
Tasos Moulinos
Derived Azumaya Algebras 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 [math]\displaystyle{ \infty }[/math]-category of [math]\displaystyle{ KU }[/math]-modules. In this talk I describe a relative version of this construction; namely for [math]\displaystyle{ X }[/math] a quasi-compact, quasi-separated [math]\displaystyle{ \mathbb{C} }[/math]-scheme I construct a functor valued in the [math]\displaystyle{ \infty }[/math]-category of sheaves of spectra on [math]\displaystyle{ X(\mathbb{C}) }[/math], the complex points of [math]\displaystyle{ X }[/math]. For inputs of the form [math]\displaystyle{ \operatorname{Perf}(X, A) }[/math] where [math]\displaystyle{ A }[/math] is an Azumaya algebra over [math]\displaystyle{ X }[/math], I characterize the values of this functor in terms of the twisted topological K-theory of [math]\displaystyle{ X(\mathbb{C}) }[/math]. From this I deduce a certain decomposition, for [math]\displaystyle{ X }[/math] a finite CW-complex equipped with a bundle [math]\displaystyle{ P }[/math] of projective spaces over [math]\displaystyle{ X }[/math], of [math]\displaystyle{ KU(P) }[/math] in terms of the twisted topological K-theory of [math]\displaystyle{ X }[/math] ; 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