Resumen de Constructible sheaves are holonomic

A. Beilinson

• 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