The Hall algebra of a curve

• Mikhail Kapranov ^[1] ; Olivier Schiffmann ^[2] ; Eric Vasserot ^[2]
  1. [1] Kavli IPMU
  2. [2] Université Paris
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 23, Nº. 1, 2017, págs. 117-177
• Idioma: inglés
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• Resumen

  • Let X be a smooth projective curve over a finite field. We describe H, the full Hall algebra of vector bundles on X, as a Feigin–Odesskii shuffle algebra.

    This shuffle algebra corresponds to the scheme S of all cusp eigenforms and to the rational function of two variables on S coming from the Rankin–Selberg L-functions.

    This means that the zeroes of these L-functions control all the relations in H. The scheme S is a disjoint union of countably many Gm-orbits. In the case when X has a theta-characteristic defined over the base field, we embed H into the space of regular functions on the symmetric powers of S.