On the generic behavior of decomposition morphisms
Ulrich Thiel (University of Stuttgart)
Wednesday 21st January, 2015 16:00-17:00 Maths 516
In my talk I will address a natural geometric question emerging when trying to compare the specialization A(0)=A^K of a finite-dimensional algebra over a normal noetherian ring R with quotient field K in the generic point (0) of Spec(R) to an arbitrary specialization A(P) in a prime ideal P of R. I will show that in case A(P) splits for all P, the Grothendieck groups of A^K and A(P) are the same (in a precise sense) on an open subset of Spec(R), where the connection between the Grothendieck groups is set up by decomposition morphisms as defined by Geck-Rouquier. This result is a nice tool for studying algebras involving parameters like Hecke algebras and Cherednik algebras. The proof uses both algebraic and topological arguments.