Topology Seminar: Ben Williams
Topic
Period & Index in Locally Ringed Topoi
Speakers
Details
In an Exposé published in 1968, Alexander Grothendieck generalized the notion of a central simple algebra over a field by defining Azumaya algebras in locally ringed topoi. Specific examples of Azumaya algebras in locally ringed topoi include (up to isomorphism) principal PUn or POn bundles on CW complexes, as well as Azumaya algebras over commutative rings. If the topos is connected, it is possible to define two invariants of an Azumaya algebra, the period & the index, which measure the nontriviality of the algebra. It is a classical theorem that the period & index have the same prime divisors in the case of central simple algebras over a field, and this is also known in the case of PUn bundles over CW complexes. In this talk, I will show that in the case of any locally ringed topos, the period & index have the same prime divisors.
Additional Information
Location: ESB 2012
Please note the change in time and location.
Ben Williams (UBC)
Ben Williams (UBC)
This is a Past Event
Event Type
Scientific, Seminar
Date
January 22, 2014
Time
-
Location