Constructible sheaves are holonomic

• A. Beilinson ^[1]
  1. [1] University of Chicago

     University of Chicago

     City of Chicago, Estados Unidos

     
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 22, Nº. 4 (Special Issue: The Mathematics of Joseph Bernstein), 2016, págs. 1797-1819
• Idioma: inglés
• DOI: 10.1007/s00029-016-0260-z
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• Resumen

  • Kashiwara and Shapira [5], motivated by the theory of holonomic D-modules, have shown that for any constructible sheaf F on a complex manifold X each component of its singular support SS(F) has dimension dim X. Here SS(F) is the smallest closed conical subset of the cotangent bundle T ∗X, such that (locally on X) every function f with d f disjoint from SS(F) is locally acyclic relative to F. In this article we establish a similar result for étale constructible sheaves on algebraic varieties over an arbitrary base field k. Our tools are Brylinski’s Radon transform [1] (which is a global algebro-geometric version of the quantized canonical transformations from [8]) and a version of the Lefschetz pencils story [6].

    As was observed by Deligne [3], if the characteristic of k is finite then, in contrast to the characteristic zero case (either for constructible sheaves or D-modules), the components of SS(F) need not be Lagrangian (see examples in 1.5 below).

    Recently Takeshi Saito [7] defined the characteristic cycle CC(F), i.e., equipped the components of SS(F) with multiplicities, and established its basic local and global