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arXiv · 2201.00559

Hida theory for special orders

Luca Dall'Ava
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Abstract

This note is devoted to the study of families of quaternionic modular forms arising from orders defined by Pizer. In this situation, the Hecke-eigenspaces are 2-dimensional contrary to the classical case of Eichler orders. The main result is a Control Theorem in the spirit of Hida, interpolating these 2-dimensional Hecke-eigenspaces. We restrict our attention to a definite rational quaternion algebra ramified at a single odd prime $\ell$.

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Luca Dall'Ava. 2022-01-03. Hida theory for special orders. https://arxiv.org/abs/2201.00559

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