McGill University, December 4 - 7, 2015
Has a charming "Massey spell" been cast on Galois $p$-extensions of general fields?
I will discuss this possibility by reviewing some of the work of M. Hopkins and K. Wickelgren, I. Efrat and E. Matzri, and my joint work with N. D. Tan. Some previous related work of S. Chebolu, I. Efrat, and myself; will also be recalled.
In my talk I will show how to extend the classical theory to a theory of cohomological invariants for Deligne-Mumford stacks and in particular for the stacks of smooth genus g curves. The concept of general cohomological invariants turns out to be closely tied to the theory of unramified cohomology, which was introduced by Saltman, Ojanguren and Colliot-Thélène and is widely used to study rationality problems.
I will also show how to compute the additive structure of the ring of cohomological invariants for the algebraic stacks of hyperelliptic curves of all even genera and genus three.