Seminars & Colloquia Calendar

Algebra Seminar

Degree One Milnor K-Invariants of Groups of Multiplicative Type

Oct Alex Wertheim (UCLA)

Location:  https://rutgers.zoom.us/j/95075528338
Date & time: Wednesday, 21 October 2020 at 2:00PM - 3:00PM

Many important algebraic objects can be viewed as $$G$$-torsors over a field $$F$$, where $$G$$ is an algebraic group over $$F$$. For example, there is a natural bijection between F-isomorphism classes of central simple $$F$$-algebras of degree $$n$$ and $$PGL_n(F)$$-torsors over Spec$$(F)$$. Much as one may study principal bundles on a manifold via characteristic classes, one may likewise study $$G$$-torsors over a field via certain associated Galois cohomology classes. This principle is made precise by the notion of a cohomological invariant, which was first introduced by Serre.

In this talk, we will determine the cohomological invariants for algebraic groups of multiplicative type with values in $$H^1(-, Q/Z(1))$$. Our main technical analysis will center around a careful examination of $$mu_n$$-torsors over a smooth, connected, reductive algebraic group. Along the way, we will compute a related group of invariants for smooth, connected, reductive groups

For the meeting password, email Ian at:
iacoley@math.rutgers.edu.

Special Note to All Travelers

Directions: map and driving directions. If you need information on public transportation, you may want to check the New Jersey Transit page.

Unfortunately, cancellations do occur from time to time. Feel free to call our department: 848-445-6969 before embarking on your journey. Thank you.