The Hall algebra of a curve

摘要: Let X be a smooth projective curve over finite field. We describe H, the full Hall algebra of vector bundles on X, as Feigin–Odesskii shuffle algebra. This corresponds to scheme S all cusp eigenforms and rational function two variables coming from Rankin–Selberg L-functions. means that zeroes these L-functions control relations in H. The is disjoint union countably many \({\mathbb G}_m\)-orbits. In case when has theta-characteristic defined base field, we embed H into space regular functions symmetric powers S.