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)