2016/07/02 by Simon Schieder, Schieder, Simon · 1 citation
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Number Theory (math.NT) #Representation Theory (math.RT) #math.AG #math.NT #math.RT
paper · pdf · doi:10.48550/arxiv.1607.00586
49 pages
openalex publication_date 2016/07/02 · arxiv created 2017/01/08 · arxiv updated 2017/01/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We define and study the Drinfeld-Lafforgue-Vinberg compactification of the moduli stack of G-bundles BunG for an arbitrary reductive group G; its definition is given in terms of the Vinberg semigroup of G, and is due to Drinfeld (unpublished). Throughout the article we prefer to view the compactification as a canonical multi-parameter degeneration of BunG which we call the Drinfeld-Lafforgue-Vinberg degeneration VinBunG. We construct local models for the degeneration VinBunG which "factorize in families" and use them to study its singularities, generalizing results of the article [Sch1] which was confined with the case G = SL2. The multi-parameter degeneration VinBunG gives rise to, for each parabolic of G, a corresponding nearby cycles functor. Our main theorem expresses the stalks of these nearby cycles in terms of the cohomology of the parabolic Zastava spaces. From this description we deduce that the nearby cycles of VinBunG correspond, under the sheaf-function correspondence, to Bernstein's asymptotics map on the level of functions. This had been speculated by Bezrukavnikov-Kazhdan [BK] and Chen-Yom Din [CY] and conjectured in a precise form by Sakellaridis [Sak2].