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arXiv · 2209.03717

Generalised theta operators on unitary Shimura varieties

Lorenzo La Porta
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Abstract

The main result of this paper is the construction of a new class of weight shifting operators, similar to the theta operators of arXiv:1902.10911, arXiv:1712.06969 and others, which are defined on the lower Ekedahl-Oort strata of the geometric special fibre of unitary Shimura varieties of signature $(n-1, 1)$ at a good prime $p$, split in the in the reflex field $E$, which we assume to be quadratic imaginary. These operators act on certain graded sheaves which are obtained from the arithmetic structure of the EO strata, in particular the $p$-rank on each stratum. We expect these operators to have applications to the study of Hecke-eigensystems of modular forms modulo $p$ and generalisations of the weight part of Serre's conjecture.

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Lorenzo La Porta. 2022-09-08. Generalised theta operators on unitary Shimura varieties. https://arxiv.org/abs/2209.03717

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