论文标题
代数和非代数重量的几何模块
Geometric modularity for algebraic and non-algebraic weights
论文作者
论文摘要
在这篇简短的论文中，我们概括了钻石的结果 - sasaki将代数重量的几何模块化连接到非代数重量的几何模块性，反之亦然。特别是，我们表明非代数权重的几何模块性意味着多个代数重量的几何模块性，这很容易看出。更重要的是，我们表明多个代数重量的几何模块有时意味着非代数重量的几何模块。这将钻石的作品 - 萨萨基（Sasaki）与早期在塞雷（Serre）猜想的重量部分的概括方面进行了工作。
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.
