EVENT DETAILS AND ABSTRACT

Title: On Galois groups of pro-p extensions with restricted ramification
Speaker: Romyar Sharafi
Speaker Info: Arizona
Brief Description:
Special Note:
Abstract:

I will give a survey of older and newer applications of a cup product pairing in the Galois cohomology of cyclotomic fields with restricted ramification to the structure of certain Iwasawa modules and pro-p Galois groups. This pairing has long been a focus of my research and was first considered in work with W. McCallum. Various conjectures have been formulated that, in particular, relate its values to Manin symbols in the homology of modular curves. These conjectures are now proven under mild conditions by T. Fukaya and K. Kato. This talk will focus on a few of the consequences of those conjectures.