WebMar 24, 2024 · Take K a number field and m a divisor of K. A congruence subgroup H is defined as a subgroup of the group of all fractional ideals relative prime to m (I_K^m) … The Weil group of a class formation with fundamental classes uE/F ∈ H (E/F, A ) is a kind of modified Galois group, used in various formulations of class field theory, and in particular in the Langlands program. If E/F is a normal layer, then the (relative) Weil group WE/F of E/F is the extension 1 → A → WE/F → Gal(E/F) … See more In mathematics, a Weil group, introduced by Weil (1951), is a modification of the absolute Galois group of a local or global field, used in class field theory. For such a field F, its Weil group is generally denoted WF. There also … See more For a local field of characteristic p > 0, the Weil group is the subgroup of the absolute Galois group of elements that act as a power of the Frobenius automorphism on the constant field (the union of all finite subfields). For p-adic fields the … See more For number fields there is no known "natural" construction of the Weil group without using cocycles to construct the extension. The map from the Weil group to the Galois group is … See more For archimedean local fields the Weil group is easy to describe: for C it is the group C of non-zero complex numbers, and for R it is a non-split extension of the Galois group of … See more For finite fields the Weil group is infinite cyclic. A distinguished generator is provided by the Frobenius automorphism. Certain conventions on terminology, such as arithmetic Frobenius, trace back to the fixing here of a generator (as the Frobenius or its … See more For global fields of characteristic p>0 (function fields), the Weil group is the subgroup of the absolute Galois group of elements that act as a power of the Frobenius … See more The Weil–Deligne group scheme (or simply Weil–Deligne group) W′K of a non-archimedean local field, K, is an extension of the Weil group WK by a one-dimensional … See more
Class field theory for function fields and a curious statement
WebApr 26, 2006 · I will speak on class field theory in higher dimensions, following Kato and Parshin. Given a sufficiently strong cohomological version of class field theory, I will … WebMay 21, 2024 · The Weil-Deligne representation is trivial on 1 + pZp ⊂ Q × p, π has a fixed vector under 1 + pZp. The corresponding l -adic representations are tamely ramified on inertia. I honestly only found very few papers in the literature in which "tamely ramified" was implied to have the meaning (1), (2), or (3). rapidsketch
Weil groups and $F$-isocrystals - ResearchGate
WebThis classic book, originally published in 1968, is based on notes of a year-long seminar the authors ran at Princeton University. The primary goal of the book was to give a rather … WebOct 16, 2024 · This chapter develops the basic structure theory for local and global fields; we follow A. Weil in stressing the topological rather than algebraic perspective, although perhaps less emphatically. WebThe primary goal of the book was to give a rather complete presentation of algebraic aspects of global class field theory ... In this revised edition, two mathematical additions complementing the exposition of the original text are made. ... Group Extensions . 127: Abstract Class Field Theory . 143: Weil Groups . 167: Bibliography . 191 ... drogazito