2015/12/17 by Dorin Boger, Boger, Dorin
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.1512.05735
openalex publication_date 2015/12/17 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
Let k be an algebraically closed field of characteristic p>>0. Let X→ Y be a symplectic resolution. There are two questions which motivates this work. One question is a construction of an action of a group on the category C:=Db(Coh(X)) - The bounded derived category of coherent sheaves of the symplectic resolution X. Second question is understanding equivalence functors between derived categories of coherent sheaves for different symplectic resolutions of Y. Let G/k be a reductive group. In this paper, we construct a local system on a topological space called V0ℂ with value the category Db(Coh(T^*G/P)) for a parabolic subgroup P. This induces an action of π1 V0ℂ on the category. In another paper we further explain how a refinement of this local system construction, gives an answer to the second question, showing that these equivalence functors, are parametrized by homotopy classes of maps between certain points in the base space. We also lift the result to characteristic zero.