The Period-Index Obstruction, by Catherine H. O'Neil

This paper has now appeared in Journal of Number Theory 95, 329-339 (2002) and so the preprint has been removed. In this paper we prove that the classical period-index obstruction map for elliptic curves is quadratic and given by a cup product in cohomology. Assuming full level n structure, we recover the Hilbert symbol, and indicate some applications. We also exhibit the local Tate pairing as a specialization of the obstruction map, first proved by Lichtenbaum in 1968.

Catherine H. O'Neil <coneil@math.mit.edu>