#
On Saltman's p-Adic Curves Papers

## Eric Brussel

Emory University

Spring 2009

These notes are the result of two expository lectures given by the author at the University of
Hyderabad, during the 2008-2009 conference on ``Quadratic forms, linear algebraic groups,
and Galois cohomology''.
The lectures covered Saltman's seminal work on the Brauer group of the function field
of a *p*-adic curve, in particular his results regarding period-index and cyclicity,
which are contained in the following papers.

[S1] Saltman, D. J.:
Division algebras over *p*-adic curves,
* J. Raman. Math. Soc.*, **12** (1997) 25-47.

[S1']
Saltman, D. J.:
Correction to division algebras over *p*-adic curves,
*J. Raman. Math. Soc.*, ** 13** (1998) 125-129.

[S2]
Saltman, D. J.:
Cyclic algebras over *p*-adic curves,
* J. Alg.* ** 314** no.2 (2007), 817-843.
See article

In these notes we reprove all of the main theorems in these papers, modulo some of [S2, Section 1],
expanding some proofs, consolidating some results, and providing additional background.

On Saltman's p-Adic Curves Papers
Corrected Version (April 2010)