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Cherednik algebras and Hilbert schemes in characteristic p (2006)
| Citations: | 39 - 8 self |
BibTeX
@MISC{Bezrukavnikov06cherednikalgebras,
author = {Roman Bezrukavnikov and Michael Finkelberg and Victor Ginzburg},
title = {Cherednik algebras and Hilbert schemes in characteristic p},
year = {2006}
}
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Abstract
We prove a localization theorem for the type An−1 rational Cherednik algebra Hc = H1,c(An−1) overFp, an algebraic closure of the finite field. In the most interesting special case where c ∈ Fp, we construct an Azumaya algebra Hc on Hilbn A2, the Hilbert scheme of n points in the plane, such that Γ(Hilbn A2, Hc) = Hc. Our localization theorem provides an equivalence between the bounded derived categories of Hc-modules and sheaves of coherent Hc-modules on Hilbn A2, respectively. Furthermore, we show that the Azumaya algebra splits on the formal neighborhood of each fiber of the Hilbert-Chow morphism. This provides a link between our results and those of Bridgeland, King and Reid, and Haiman.
