论文标题
在兰兰兹计划，全球领域和Shtukas上
On Langlands program, global fields and shtukas
论文作者
论文摘要
本文的目的是调查兰兰兹计划，全球领域，$ d $ shtukas和有限shtukas的一些重要结果，这些结果影响了代数和数字理论的发展。它的意图是有选择性的，而不是详尽的，因为与Yakovlev的80岁生日，Vostokov的75岁生日和Lurie的75岁生日相适应。根据兰兰兹计划的地面假设，兰格兰兹，雅克，贾克，沙法维奇，帕辛，德林菲尔德，拉福尔格等已经证明了和讨论。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$ d $ -shtukas和有限的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。
The purpose of this paper is to survey some of the important results on Langlands program, global fields, $D$-shtukas and finite shtukas which have influenced the development of algebra and number theory. It is intended to be selective rather than exhaustive, as befits the occasion of the 80-th birthday of Yakovlev, 75-th birthday of Vostokov and 75-th birthday of Lurie. Under assumptions on ground fields results on Langlands program have been proved and discussed by Langlands, Jacquet, Shafarevich, Parshin, Drinfeld, Lafforgue and others. 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 $ D $ --shtukas and finite shtukas. These approaches and our discussion relate to the Langlands program as well as to the internal development of the theory of $ G $-shtukas.
