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arXiv · 1407.1941

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

Stefan Patrikis
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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.

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Stefan Patrikis. 2014-09-05. Generalized Kuga-Satake theory and rigid local systems, II: rigid Hecke eigensheaves. https://doi.org/10.2140/ant.2016.10.1477

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