Abstract: It is a classical problem to relate the period of a Brauer class to its index. This has been carried out over certain ground fields, including by the speaker and collaborators in the case of semi-global fields; i.e. function fields of curves over a complete discretely valued field. This talk concerns an analog of this question, in which one considers higher cohomology classes rather than Brauer classes. Motivated by work of Saurabh Gosavi on Brauer groups, we also consider the simultaneous index of a finite set of cohomology classes in this context. This is joint work with Julia Hartmann and Daniel Krashen.
Ref: D. Harbater, J. Hartmann and D. Krashen, Bounding cohomology classes over semiglobal fields
