Proof of local Artin reciprocity
نویسنده
چکیده
which for every finite Galois extension L/K induces an isomorphism invL/K : H (Gal(L/K), L×) ∼ −→ 1 [L:K]Z/Z via composition with the inflation map Inf : H2(Gal(L/K), L×)→ H2(Gal(Ksep/K),Ksep×), and we showed that invK is canonical and natural in K; see Theorem 30.25 In this lecture we will use the invariant map to define the local Artin homomorphism and prove the local version of Artin reciprocity.
منابع مشابه
Conics over function fields and the Artin-Tate conjecture
We prove that the Hasse principle for conics over function fields is a simple consequence of a provable case of the Artin-Tate conjecture for surfaces over finite fields. Hasse proved that a conic over a global field has a rational point if and only if it has points over all completions of the global field, an instance of the so-called local-global or Hasse principle. The case of the rational n...
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 کامل18.785F17 Number Theory I Lecture 23 Notes: Tate Cohomology
In this lecture we introduce a variant of group cohomology known as Tate cohomology, and we define the Herbrand quotient (a ratio of cardinalities of two Tate cohomology groups), which will play a key role in our proof of Artin reciprocity. We begin with a brief review of group cohomology, restricting our attention to the minimum we need to define the Tate cohomology groups we will use. At a nu...
متن کاملArtin Reciprocity and Mersenne Primes
On March 3, 1998, the centenary of Emil Artin was celebrated at the Universiteit van Amsterdam. This paper is based on the two morning lectures, enti-tled`Artin reciprocity and quadratic reciprocity' and`Class eld theory in practice', which were delivered by the authors. It provides an elementary introduction to Artin reciprocity and illustrates its practical use by establishing a recently obse...
متن کاملArtin Reciprocity and Mersenne Primes Artin Reciprocity And
Emil Artin was born on March 3, 1898 in Vienna, as the son of an art dealer and an opera singer, and he died on December 20, 1962 in Hamburg. He was one of the founding fathers of modern algebra. Van der Waerden acknowledged his debt to Artin and to Emmy Noether (1882–1935) on the title page of his Moderne Algebra (1930–31), which indeed was originally conceived to be jointly written with Artin...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2018