D-modules and finite maps

2018/11/16 by Rolf Källström, Källström, Rolf
Mathematics · #14 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra (math.AC) #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1811.06796

openalex publication_date 2018/11/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the preservation of semisimplicity for holonomic D-modules with respect to the direct and inverse image of mainly finite maps π: X → Y of smooth varieties. A natural filtration of the direct image π₊(\mathcal O_X) is defined by the vanishing of local cohomology along a natural stratification of π. The notions are exemplified with the invariant map X→ X^G, where G is a complex reflection group. Simply connected varieties are treated algebraically by considering connections instead of fundamental groups. For example, a "Grothendieck-Lefschetz" theorem for connections is proven and also a generalized version of the assertion that rationally connected varieties be simply connected, entirely by algebraic means, using the idea of a "differential covering".

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