论文标题
在Langlands计划，相关代表和$ G $ -SHTUKAS上
On Langlands program, related representation and $G$-shtukas
论文作者
论文摘要
这种交流是兰格兰计划和（$ g $ - ）shtukas（代数曲线）的介绍。模块化曲线和德林菲尔德（椭圆形）模块和shtukas用于编码理论。从这个角度来看，交流与编码理论的数学模型和方法有关。对于全球字段$ k $的连接的还原组$ g $，Langlands通信与$ G $和全球Langlands参数的自动形式相关联，即来自Galois Group $ {\ Mathcal Gal}（\ Mathcal Gal}（{\ edline kypline k} / k g g g g lline the the the the the the the the the the the complline the the complline the the complline the complline the dual dual langlang langlangs dual lang langlangs {\ Mathbb Q}} _ P）$。对于代数数字的领域，兰兰兹计划要素的应用和发展使得可以在Shimura-Taniyama-Weil假设上加强Wiles定理并证明SATO-TATE假设。在这篇评论文章中，我们首先介绍了兰兰兹计划和代数数字领域的相关表示形式。然后，我们简要介绍了U. Hartl，他的同事和学生的方法，以研究$ g $ -shtukas。这些方法和我们的讨论与兰兰兹计划以及$ g $ -shtukas理论的内部发展有关。
This communication is an introduction to the Langlands Program and to ($G$-) shtukas (over algebraic curves) over function fields. Modular curves and Drinfeld (elliptic) modules and shtukas are used in coding theory. From this point of view the communication is concerned with mathematical models and methods of coding theory. For a connected reductive group $ G $ over a global field $ K $, the Langlands correspondence relates automorphic forms on $ G $ and global Langlands parameters, i.e. conjugacy classes of homomorphisms from the Galois group $ {\mathcal Gal} ({\overline K} / K) $ to the dual Langlands group $ \hat G ({\overline {\mathbb Q}}_p) $. In the case of fields of algebraic numbers, the application and development of elements of the Langlands program made it possible to strengthen the Wiles theorem on the Shimura-Taniyama-Weil hypothesis and to prove the Sato-Tate hypothesis. In this review article, we first present results on Langlands program and related representation over algebraic number fields. Then we briefly present approaches by U. Hartl, his colleagues and students to the study of $ G $ --shtukas. These approaches and our discussion relate to the Langlands program as well as to the internal development of the theory of $ G $-shtukas.
