Results 11 to 20 of about 19,332,303 (287)

Class Formations and Higher Dimensional Local Class Field Theory [PDF]

Journal of Number Theory, 1997
Let \(K\) be an \(n\)-local field, \(K^M_n(K)\) the \(n\)-th Milnor \(K\)-group of \(K\). Furthermore, let \(G_K^{ab}\) be the Galois group of the maximal abelian extension of \(K\). The reciprocity map is a canonical homomorphism from \(K_n^M(K)\) in \(G_K^{ab}\) which for every finite abelian extension \(L/K\) induces an isomorphism \(K_n^M(K)/ N_{L ...
Michael Spiess
exaly   +5 more sources

Class field theory for curves over local fields [PDF]

Journal of Number Theory, 1985
Let \(X\) be a smooth projective geometrically irreducible curve over a local field \(k\). The purpose of this paper is to develop unramified class theory for \(X\), i.e. to try to approximate the abelian fundamental group \(\pi_ 1^{ab}(X)\) which controls the abelian étale covers of \(X\) by means of some group defined ``downstairs''. \textit{S. Bloch}
Saito, Shuji
exaly   +5 more sources

Class field theory for curves over local fields [PDF]

, 2023
We establish a ramified class field theory for smooth projective curves over local fields. As key steps in the proof, we obtain new results in the class field theory for 2-dimensional local fields of positive characteristic, and prove a duality theorem for the logarithmic Hodge-Witt cohomology on affine curves over local fields.
Krishna, Amalendu, Majumder, Subhadip
core   +4 more sources

Tame class field theory over local fields [PDF]

, 2022
Substantial revision, 68 pages. A version of this paper is accepted to appear in Amer.
Gupta, Rahul, Krishna, Amalendu, Rathore, Jitendra   +2 more
openaire   +3 more sources

Local Class Field Theory via Lubin-Tate Theory [PDF]

Annales de la Faculté des sciences de Toulouse : Mathématiques, 2008
We give a self-contained exposition of local class field theory, via Lubin-Tate theory and the Hasse-Arf theorem, refining the arguments of Iwasawa [9].
Mohamed, Adam
openaire   +4 more sources

Local class field theory is easy

Advances in Mathematics, 1975
Let K be a local field with finite residue field. For the purposes of this paper, “local class field theory” consists of the (more or less) explicit description of the maximal abelian extension Kab of K, of the calculation of the galois group Gal(K,,/K); i.e., the proof that Gal(KJK) N K*, the completion of K* with respect to the topology given by the ...
openaire   +5 more sources

Local non-abelian class field theory [PDF]

Hacettepe Journal of Mathematics and Statistics
The ``local class field theory'', which can be defined as the description of the extensions of a given local field $K$ with finite residue field of $q=p^f$ elements in terms of the algebraic and analytic objects depending only on the base $K$ is one of the central problems of modern number theory. The theory developed for the abelian extensions, around
Bedikyan, Sevan
openaire   +3 more sources

Finiteness theorems in the class field theory of varieties over local fields

Journal of Number Theory, 2003
Let \(K\) be a finite extension of \({\mathbb Q}_p\) or of \({\mathbb F}_{p}((T))\) (\(p\) prime), and let \(X\) be a smooth proper absolutely connected \(K\)-variety. Denote by \(\varpi_1(X)\) the maximal commutative quotient of the profinite group \(\pi_1(X)\), the étale fundamental group of \(X\).
openaire   +3 more sources

Diluted mass gap in strongly coupled non-local Yang-Mills

Journal of High Energy Physics, 2021
We investigate the non-perturbative regimes in the class of non-Abelian theories that have been proposed as an ultraviolet completion of 4-D Quantum Field Theory (QFT) generalizing the kinetic energy operators to an infinite series of higher-order ...
Marco Frasca, Anish Ghoshal
doaj   +1 more source

General Fractional Noether Theorem and Non-Holonomic Action Principle

Mathematics, 2023
Using general fractional calculus (GFC) of the Luchko form and non-holonomic variational equations of Sedov type, generalizations of the standard action principle and first Noether theorem are proposed and proved for non-local (general fractional) non ...
Vasily E. Tarasov
doaj   +1 more source