# Difference between revisions of "Algebraic Geometry Seminar Spring 2018"

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|Dima | |Dima | ||

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− | | | + | |April 6 |

|[http://www-personal.umich.edu/~ptoste/ Phil Tosteson (Michigan)] | |[http://www-personal.umich.edu/~ptoste/ Phil Tosteson (Michigan)] | ||

|[[#Phil Tosteson|TBA]] | |[[#Phil Tosteson|TBA]] | ||

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== Abstracts == | == Abstracts == | ||

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+ | ===Tasos Moulinos=== | ||

+ | |||

+ | '''Derived Azumaya Algebras and Twisted K-theory''' | ||

+ | |||

+ | Topological K-theory of dg-categories is a localizing invariant of dg-categories over <math> \mathbb{C} </math> | ||

+ | taking values in the <math> \infty </math>-category of <math> KU </math>-modules. In this talk I describe a relative version | ||

+ | of this construction; namely for <math>X</math> a quasi-compact, quasi-separated <math> \mathbb{C} </math>-scheme I construct a | ||

+ | functor valued in the <math> \infty </math>-category of sheaves of spectra on <math> X(\mathbb{C}) </math>, the complex points of <math>X</math>. For inputs | ||

+ | of the form <math>\operatorname{Perf}(X, A)</math> where <math>A</math> is an Azumaya algebra over <math>X</math>, I characterize the values | ||

+ | of this functor in terms of the twisted topological K-theory of <math> X(\mathbb{C}) </math>. From this I deduce | ||

+ | a certain decomposition, for <math> X </math> a finite CW-complex equipped with a bundle <math> P </math> of projective | ||

+ | spaces over <math> X </math>, of <math> KU(P) </math> in terms of the twisted topological K-theory of <math> X </math> ; this is | ||

+ | a topological analogue of a result of Quillen’s on the algebraic K-theory of Severi-Brauer | ||

+ | schemes. | ||

===Aron Heleodoro=== | ===Aron Heleodoro=== |

## Revision as of 10:27, 17 January 2018

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

Here is the schedule for the previous semester.

## Contents

## 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 |

April 6 | 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 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.

### Aron Heleodoro

**TBA**

### Alexander Yom Din

**TBA**