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arXiv · 2205.00946

Geometric modularity for algebraic and non-algebraic weights

Hanneke Wiersema
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Abstract

In this short paper we generalise a result of Diamond--Sasaki connecting geometric modularity of algebraic weights to geometric modularity of non-algebraic weights and vice versa. In particular, we show that geometric modularity of non-algebraic weights implies geometric modularity of multiple algebraic weights, which is easy to see. More significantly, we show that geometric modularity of multiple algebraic weights sometimes implies geometric modularity of a non-algebraic weight. This connects work of Diamond--Sasaki to earlier work on generalisations of the weight part of Serre's conjecture.

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Hanneke Wiersema. 2022-05-02. Geometric modularity for algebraic and non-algebraic weights. https://arxiv.org/abs/2205.00946

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