WHAT IS ...the Langlands Program?
نویسندگان
چکیده
منابع مشابه
Prerequisites for the Langlands Program∗
For learning about the Langlands program, knowledge of Lie-group structure theory, algebraic number theory, algebraic geometry, modular forms, and infinite-dimensional representation theory is appropriate. This article describes how one can get a glimpse of the program with less background than this.
متن کاملIntroduction to the Langlands Program
This article is an introduction to automorphic forms on the adeles of a linear reductive group over a number field. The first half is a summary of aspects of local and global class field theory, with emphasis on the local Weil group, the L functions of Artin and Hecke, and the role of Artin reciprocity in relating the two kinds of L functions. The first half serves as background for the second ...
متن کاملFirst Steps with the Langlands Program∗
This article describes ways in which to get an overview of some of the goals and methods of Langlands program, and it points to treatments of some examples that are worth keeping in mind.
متن کاملGauge Theory and the Geometric Langlands Program
The Langlands program of number theory, or what we might call Langlands duality, was proposed in more or less its present form by Robert Langlands, in the late 1960s. It is a kind of unified scheme for many results in number theory ranging from quadratic reciprocity, which is hundreds of years old, to modern results such as Andrew Wiles’ proof of Fermat’s last theorem, which involved a sort of ...
متن کاملRecent Advances in the Langlands Program
The Langlands Program has emerged in the late 60’s in the form of a series of far-reaching conjectures tying together seemingly unrelated objects in number theory, algebraic geometry, and the theory of automorphic forms [L1]. To motivate it, consider the old question from number theory: what is the structure of the Galois group Gal(Q/Q) of the field Q of rational numbers, i.e., the group of aut...
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ژورنال
عنوان ژورنال: Notices of the American Mathematical Society
سال: 2018
ISSN: 0002-9920,1088-9477
DOI: 10.1090/noti1686