论文标题
关于Mochizuki的Anabelomorphy及其应用的想法
On Mochizuki's idea of Anabelomorphy and its applications
论文作者
论文摘要
我创造了一词的Anabelomorphy（发音为Anabel-O-Morphy），是一种表达Mochizuki的“ Anabelian改变地面田地，戒指等的方式”的简洁方式。这是他在他的全世界Teichmuller理论的工作中介绍的。本文通过在更熟悉的算术环境中研究其后果，例如Galois表示理论，自动形式和相关领域，并建立许多具有独立算术兴趣的结果，从而证明了这一想法的有用性。我还介绍了替代型连接的数字字段的概念，其中两个数字字段通过本地Galois组之间存在拓扑同构的存在相关，这两个数字字段的数量有限列表，并证明了一些结果表明了这一概念的算术后果。简介提供了本文证明的所有结果的详细讨论和摘要。
I coined the term anabelomorphy (pronounced as anabel-o-morphy) as a concise way of expressing Mochizuki's idea of "anabelian way of changing ground field, rings etc." which was he has introduced in his work on his Inter-Universal Teichmuller Theory. This paper demonstrates the usefulness of this idea by studying its ramifications in the more familiar arithmetic contexts such as the theory of Galois representations, automorphic forms and related areas and establish a number of results which are of independent arithmetic interest. I also introduce the notion of anabelomorphically connected number fields in which two number fields are related by the existence of topological isomorphism between the local Galois groups at a finite list of primes of both the number fields and prove some results illustrating arithmetic consequences of this notion. The Introduction provides a detailed discussion and summary of all the results proved in this paper.
