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arXiv · 1407.1942

Generalized Kuga-Satake theory and rigid local systems, I: the middle convolution

Stefan Patrikis
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Abstract

This note explains an approach to producing examples of 'generalized Kuga-Satake theory' based on establishing special cases of Simpson's conjecture that rigid local systems are motivic. This strategy is then carried out, using work of Bogner and Reiter, in a low-dimensional example, producing the first non-trivial examples of generalized Kuga-Satake theory outside of the Tannakian category of motives generated by abelian varieties. For a more robust collection of examples, see the sequel "Generalized Kuga-Satake theory and rigid local systems, II: rigid Hecke eigensheaves."

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Stefan Patrikis. 2014-07-08. Generalized Kuga-Satake theory and rigid local systems, I: the middle convolution. https://arxiv.org/abs/1407.1942

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