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arXiv · 2007.01752

Fixed points, local monodromy, and incompressibility of congruence covers

Patrick Brosnan·Najmuddin Fakhruddin
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Abstract

We prove a fixed point theorem for the action of certain local monodromy groups on étale covers and use it to deduce lower bounds in essential dimension. In particular, we give more geometric proofs of many (but not all) of the results of the preprint of Farb, Kisin and Wolfson, which uses arithmetic methods to prove incompressibility results for Shimura varieties and moduli spaces of curves. Our method allows us to prove results for exceptional groups, and also for the reduction modulo good primes of Shimura varieties and moduli spaces of curves.

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Patrick Brosnan, Najmuddin Fakhruddin. 2020-07-17. Fixed points, local monodromy, and incompressibility of congruence covers. https://arxiv.org/abs/2007.01752

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