Generalized Kuga-Satake theory and rigid local systems, I: the middle convolution
Number Theory
2014-07-09 v1 Algebraic Geometry
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."
Cite
@article{arxiv.1407.1942,
title = {Generalized Kuga-Satake theory and rigid local systems, I: the middle convolution},
author = {Stefan Patrikis},
journal= {arXiv preprint arXiv:1407.1942},
year = {2014}
}
Comments
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