酉群的权循环和Serre型拓扑
Weight cycling and Serre-type conjectures for unitary groups
摘要：
我们证明了U（3）的形式是紧凑的在无穷远和分裂的地方除了一个素数p，在一般情况下，一个模p的模块伽罗瓦表示的Serre重量是不可约时，限制到每个分解群以上的p正是那些先前预测的第三作者。我们这样做是通过结合明确的计算在p进霍奇理论，强可除模和Breuil模块的形式主义的基础上下降的数据，我们开发的文件，与一种技术，我们称之为“重量循环”。
英文摘要：
We prove that for forms of U(3) which are compact at infinity and split at places dividing a prime p, in generic situations the Serre weights of a mod p modular Galois representation which is irreducible when restricted to each decomposition group above p are exactly those previously predicted by the third author. We do this by combining explicit computations in p-adic Hodge theory, based on a formalism of strongly divisible modules and Breuil modules with descent data which we develop in the paper, with a technique that we call "weight cycling".
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