15 June 2012 On the Hall algebra of an elliptic curve, II
Olivier Schiffmann
Duke Math. J. 161(9): 1711-1750 (15 June 2012). DOI: 10.1215/00127094-1593362

Abstract

The Hall algebra UE+ of the category of coherent sheaves on an elliptic curve E defined over a finite field has been explicitly described and shown to be a 2-parameter deformation of the ring of diagonal invariants R+=C[x1±1,,y1,]S (in infinitely many variables). We study a geometric version of this Hall algebra, by considering a convolution algebra of perverse sheaves on the moduli spaces of coherent sheaves on E. This allows us to define a canonical basis B of UE+ in terms of intersection cohomology complexes. We also give a characterization of this basis in terms of an involution, a lattice, and a certain PBW-type basis.

Citation

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Olivier Schiffmann. "On the Hall algebra of an elliptic curve, II." Duke Math. J. 161 (9) 1711 - 1750, 15 June 2012. https://doi.org/10.1215/00127094-1593362

Information

Published: 15 June 2012
First available in Project Euclid: 6 June 2012

zbMATH: 1253.14018
MathSciNet: MR2922373
Digital Object Identifier: 10.1215/00127094-1593362

Subjects:
Primary: 22E57
Secondary: 17B37

Rights: Copyright © 2012 Duke University Press

Vol.161 • No. 9 • 15 June 2012
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