Description
Commutative Algebra seminar.
Speaker: R V Gurjar.
Affiliation: IIT Bombay.
Date and Time: Monday 30 September, 3:30 pm - 5:00 pm.
Venue: Room 215, Department of Mathematics.
Title: P. Samuel's descent theorem.
Abstract: Let R be a normal noetherian domain with a finite group of
automorphisms G. Samuel's result says that the kernel of the natural
homomorphism Cl(R^G)\to Cl(R) is a subgroup of H^1(G,U), where U is the
group of units in R.
If R is divisorially unramified over R^G then the kernel is isomorphic to
H^1(G,U). This enables us to find the divisor class groups of rings of
invariants of finite group actions on polynomial or power series rings. If
time permits two general constructions of cyclic unramified coverings of
normal varieties will be discussed.