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Class field theory describes the Abelian extensions of a local or global field in terms of the arithmetic of the field itself. The aim of this thesis is to present and prove its main statements. We begin by developing local class field theory and then we derive the global results from the local results.
Alonso Rodríguez, Raúl
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Class Field Theory and Elliptic Curves with Complex Multiplication [PDF]
openClass field theory is a branch of algebraic number theory which has the purpose of studying and classifying abelian extensions of fields. The work starts with a detailed study of this theory based on a cohomological approach which leads to the ...
DA RONCHE, ENRICO
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Class field theory, its three main generalisations, and applications [PDF]
This work presents branches of class field theory. Special and general approaches to class field theory, and their roles, are discussed. Three main generalisations of class field theory: higher class field theory, Langlands correspondences and anabelian ...
Fesenko, Ivan
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The Lockdown Diaries of the Working Class
Collated by the Working Class Collective, The Lockdown Diaries of the Working Class is a beautiful, self-published, illustrated book featuring the diaries of working class people from across the UK and their experiences of life during the first COVID19 ...
The Working Class Collective
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Algebraic field theory operads and linear quantization [PDF]
We generalize the operadic approach to algebraic quantum field theory [arXiv:1709.08657] to a broader class of field theories whose observables on a spacetime are algebras over any single-colored operad.
Bruinsma, Simen, Schenkel, Alexander
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AdS5 compactifications with punctures in massive IIA supergravity
We find AdS5 solutions holographically dual to compactifications of six- dimensional N $$ \mathcal{N} $$ = (1, 0) supersymmetric field theories on Riemann surfaces with punctures.
Ibrahima Bah +2 more
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Higher dimensional quantum Hall effect as A-class topological insulator
We perform a detail study of higher dimensional quantum Hall effects and A-class topological insulators with emphasis on their relations to non-commutative geometry.
Kazuki Hasebe
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Olympic links in a Chebotarev link
The Chebotarev law for an infinite link is an equidistribution property about how its components are linked in a group theoretic sense. We overview several properties of a Chebotarev link following the author's article "Chebotarev links are stable ...
Jun Ueki
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On a problem of Hasse and Ramachandra
Let K be an imaginary quadratic field, and let 𝔣 be a nontrivial integral ideal of K. Hasse and Ramachandra asked whether the ray class field of K modulo 𝔣 can be generated by a single value of the Weber function. We completely resolve this question when
Koo Ja Kyung +2 more
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Duality for relative logarithmic de Rham–Witt sheaves and wildly ramified class field theory over finite fields [PDF]
In order to study p-adic etale cohomology of an open subvariety U of a smooth proper variety X over a perfect field of characteristic p > 0, we introduce new p-primary torsion sheaves.
Saito, Shuji +5 more
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