Generalized Kuga-Satake theory and rigid local systems, II: rigid Hecke eigensheaves

Abstract

This paper uses rigid Hecke eigensheaves, building on Yun's work on the construction of motives with exceptional Galois groups, to produce the first robust examples of `generalized Kuga-Satake theory' outside the Tannakian category of motives generated by abelian varieties. To strengthen our description of the `motivic' nature of Kuga-Satake lifts, we digress to establish a result that should be of independent interest: for any quasi-projective variety over a (finitely-generated) characteristic zero field, the associated weight-graded of its intersection cohomology arises from a motivated motive in the sense of André, and in particular from a classical homological motive if one assumes the Standard Conjectures. This extends work of de Cataldo and Migliorini.

minor revisions to previous version. comments welcome

References in corpus (3)

• Automorphy and irreducibility of some l-adic representations
• The projectors of the decomposition theorem are motivic
• Generalized Kuga-Satake theory and rigid local systems, I: the middle convolution

Cited by in corpus (1)

• Generalized Kuga-Satake theory and good reduction properties of Galois representations