Cherednik algebras and Hilbert schemes in characteristic p

Details Cherednik algebras and Hilbert schemes in characteristic p Cherednik algebras and Hilbert schemes in characteristic p

2003-12-29

arxiv.org/abs/math/0312474v5

Mathematics

Representation Theory

Appendices by Pavel Etingof and Vadim Vologodsky

Scientific paper

We prove a localization theorem for the type A rational Cherednik algebra H_c=H_{1,c} over an algebraic closure of the finite field F_p. In the most interesting special case where the parameter c takes values in F_p, we construct an Azumaya algebra A_c on Hilb^n, the Hilbert scheme of n points in the plane, such that the algebra of global sections of A_c is isomorphic to H_c. Our localisation theorem provides an equivalence between the bounded derived categories of H_c-modules and sheaves of coherent A_c-modules on the Hilbert scheme, respectively. Furthermore, we show that the Azumaya algebra splits on the formal completion of each fiber of the Hilbert-Chow morphism. This provides a link between our results and those of Bridgeland-King-Reid and Haiman.

Affiliated with

Also associated with

No associations

Rating

Cherednik algebras and Hilbert schemes in characteristic p does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Cherednik algebras and Hilbert schemes in characteristic p, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Cherednik algebras and Hilbert schemes in characteristic p will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-717708