The characteristic cycle and the singular support of a constructible sheaf
By Takeshi Saito. 2015
95 citations recorded by the source corpus.
We define the characteristic cycle of an étale sheaf as a cycle on the cotangent bundle of a smooth variety in positive characteristic using the singular support recently defined by Beilinson. We prove a formula à la Milnor for the total dimension of the space of vanishing cycles and an index formula computing the Euler–Poincaré characteristic, generalizing the Grothendieck–Ogg–Shafarevich formula to higher dimension. An essential ingredient of the construction and the proof is a partial generalization to higher dimension of the semi-continuity of the Swan conductor due to Deligne–Laumon. We prove the index formula by establishing certain functorial properties of characteristic cycles.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/1a06d5edd841b7026db7d60cb73925bc2513d22e
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In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- Constructible sheaves are holonomic (2015, background): “e 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 [S] defined the characteristic cycle CC(F), i.e., equipped the components of SS(F) with multiplicitie”