# Algebra Seminar

Current contacts: Vasily Dolgushev, Ed Letzter or Martin Lorenz.

The Seminar usually takes place on Mondays at 1:30 PM in Room 617 on the sixth floor of Wachman Hall. Click on title for abstract.

• Monday February 25, 2019 at 13:30, Wachman 617
Prime Torsion of the Brauer Group of an Elliptic Curve

Charlotte Ure, Michigan State University

The Brauer group of an elliptic curve $E$ is an important invariant with intimate connections to cohomology and rational points. Elements of this group can be described as Morita equivalence classes of central simple algebras over the function field. The Merkurjev-Suslin theorem implies that these classes can be written as tensor product of symbol (or cyclic) algebras. In this talk, I will describe an algorithm to calculate generators and relations of the $q$-torsion ($q$ a prime) of the Brauer group of $E$ in terms of these tensor products over any field of characteristic different from $2$,$3$, and $q$, containing a primitive $q$-th root of unity. This is work in progress.

• Monday January 28, 2019 at 13:30, Wachman 617
Paschke Categories, K-homology and the Riemann-Roch Transformation

Khashayar Sartipi, University of Illinois at Chicago

For a separable C^*-algebra A, we introduce an exact C^*-category called the Paschke Category of A, which is completely functorial in A, and show that its K-theory groups are isomorphic to the topological K-homology groups of the C^*-algebra A. Then we use the Dolbeault complex and ideas from the classical methods in Kasparov K-theory to construct an acyclic chain complex in this category, which in turn, induces a Riemann-Roch transformation in the homotopy category of spectra, from the algebraic K-theory spectrum of a complex manifold X, to its topological K-homology spectrum. This talk is based on the preprint https://arxiv.org/abs/1810.11951