Stable models of Hecke operators

Jan Vonk

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arXiv · 1501.03488

Stable models of Hecke operators

Jan Vonk

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Abstract

We investigate the geometry of correspondences between curves, and prove that correspondences over a non-Archimedean valued field have potentially stable reduction, generalising and strengthening results of Coleman and Liu. This yields a concrete description of the operator on the cohomology of the generic fibres arising from linearisation of the correspondence, via the weight-monodromy filtration and Picard-Lefschetz theory. We explicitly determine stable models of Hecke operators on various quaternionic Shimura curves, and prove a generalisation of the geometric theory of canonical subgroups by Goren and Kassaei.

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Jan Vonk. 2015-01-14. Stable models of Hecke operators. https://arxiv.org/abs/1501.03488

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