The four operations on perverse motives

Por • 2 mar, 2019 • Sección: Leyes

Florian Ivorra, Sophie Morel

Let k be a field of characteristic zero with a fixed embedding σ:k↪C into the field of complex numbers. Given a k-variety X, we use the triangulated category of étale motives with rational coefficients on X to construct an abelian category M(X) of perverse mixed motives. We show that over Spec(k) the category obtained is canonically equivalent to the usual category of Nori motives and that the derived categories Db(M(X)) are equipped with the four operations of Grothendieck (for morphisms of quasi-projective k-varieties) as well as nearby and vanishing cycles functors.  In particular, as an application, we show that many classical constructions done with perverse sheaves, such as intersection cohomology groups or Leray spectral sequences, are motivic and therefore compatible with Hodge theory. This recovers and strenghtens works by Zucker, Saito, Arapura and de Cataldo-Migliorini and provide an arithmetic proof of the pureness of intersection cohomology with coefficients in a geometric variation of Hodge structures.

arXiv:1901.02096v1 [math.AG]

Algebraic Geometry (math.AG); Number Theory (math.NT)

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