##### Department of Mathematics,

University of California San Diego

****************************

### Math 209 - Number Theory

## Asher Auel

#### University of Pennsylvania

## Cohomological Invariants of Line Bundle-Valued Forms

##### Abstract:

Over an algebraic variety, vector bundles with a symmetric bilinear form, taking values in a possibly non-trivial line bundle, are of increasing interest in arithmetic geometry. These are the natural objects on which to define generalized trace maps. However, until recently these forms have not enjoyed a theory of cohomological invariants analogous to the Hasse-Witt invariants (when the line bundle is trivial). I will give some arithmetic situations where line bundle-valued forms arise, and I will survey the construction of new invariants for these forms in "mod 4" etale cohomology.

Host: Cristian Popescu

### November 12, 2008

### 3:00 PM

### AP&M 5402

****************************