Cherednik algebras and Hilbert schemes in characteristic p

By R. Bezrukavnikov, Michael Finkelberg, V. Ginzburg. 2003

69 citations recorded by the source corpus.

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.

View Paper: https://www.semanticscholar.org/paper/2311d516fa630c74c7bebc8b712b6f18e7b7bdbc

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Citations in the corpus

Microlocalization of rational Cherednik algebras (2007, background): “290 pp. [6] Etingof, Pavel and Ginzburg, Victor, Symplectic reflection algebras, Calogero-Moser space, and de- formed Harish-Chandra homomorphism, Invent.”
Symplectic reflection algebras (2007, background): “These include positive characteristic, [16], [102], [24]; continuous Hecke algebras, [49], [115]; generalisations of Schur– Weyl duality, [84], [85], [86]; connections with affine Lie algebras, [2]; Cherednik algebras for varieties with group actions, [46]; relations with Hopf algebras, [4]; real al”
Refined knot invariants and Hilbert schemes (2013, methodology): “In characteristicp, the analogous construction has been carried out by Bezrukavnikov-Finkelberg-Ginzburg ([7]).”