2006/05/04 by Anton Braverman, Braverman, A., Dennis Gaitsgory +1
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.math/0605139
openalex publication_date 2006/05/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31
Let X be a (smooth and complete) curve and G a reductive group. In [BG] we introduced the object that we called "geometric Eisenstein series". This is a perverse sheaf EisE (or rather a complex of such) on the moduli stack BunG(X) of principal G-bundles on X, which is attached to a local system E on X with respect to the torus \checkT, Langlands dual to the Cartan subgroup T⊂ G. In loc. cit. we showed thatEisE corresponds to the \checkG-local system induced from E, in the sense of the geometric Langlands correspondence. In the present paper we address the following question, suggested by V. Drinfeld: what is the perverse sheaf on BunG(X) that corresponds to the universal deformation of E as a local system with respect to the Borel subgroup \checkB⊂ \checkG? We prove, following a conjecture of Drinfeld, that the resulting perverse sheaf if the classical, i.e., non-compactified Eisenstein series.