Results 1 to 10 of about 6,242 (64)
Hopf Galois theory for separable field extensions
Journal of Algebra, 1987 The concept of an extension \(S\supseteq R\) of commutative rings being an \(H\)-Galois extension for some Hopf \(R\)-algebra \(H\) has been available since the work of \textit{S. U. Chase} and \textit{M. E. Sweedler} [Hopf algebras and Galois theory. Lect. Notes Math. 97.
Pareigis, Bodo, Greither, C.
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Hopf Galois theory of separable field extensions [PDF]
, 2016 Hopf Galois theory is a generalization of Galois theory. Galois theory gives a bijective correspondence between intermediate fields of a Galois field extension (normal and separable) and subgroups of the Galois group. Hopf Galois theory substitutes the Galois group by a Hopf algebra.
Salguero Garcı́a, Marta
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Random Galois extensions of Hilbertian fields [PDF]
, 2012 Let L be a Galois extension of a countable Hilbertian field K.
Bary-Soroker, Lior, Fehm, Arno
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From Galois to Hopf Galois: theory and practice
, 2014 Hopf Galois theory expands the classical Galois theory by considering the Galois property in terms of the action of the group algebra k[G] on K/k and then replacing it by the action of a Hopf algebra.
Crespo, Teresa +2 more
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Mathematika, Volume 72, Issue 2, April 2026.Abstract In this paper, we study traces of Hecke operators on Drinfeld modular forms of level 1 in the case A=Fq[T]$A = \mathbb {F}_q[T]$. We deduce closed‐form expressions for traces of Hecke operators corresponding to primes of degree at most 2 and provide algorithms for primes of higher degree.
Sjoerd de Vries
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Class field theory for strictly quasilocal fields with Henselian discrete valuations
, 2006 The paper establishes a relationship between finite separable extensions and norm groups of strictly quasilocal fields with Henselian discrete valuations, which yields a generally nonabelian one-dimensional local class field theory.Comment: 14 pages ...
Chipchakov, I. D.
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Journal of the London Mathematical Society, Volume 113, Issue 3, March 2026.Abstract Number theory for positive characteristic contains analogues of the special values that were introduced by Carlitz; these include the Carlitz gamma values and Carlitz zeta values. These values were further developed to the arithmetic gamma values and multiple zeta values by Goss and Thakur, respectively.
Ryotaro Harada, Daichi Matsuzuki
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Galois extensions of Lubin-Tate spectra
, 2008 Let E_n be the n-th Lubin-Tate spectrum at a prime p. There is a commutative S-algebra E^{nr}_n whose coefficients are built from the coefficients of E_n and contain all roots of unity whose order is not divisible by p.
Andrew Baker +2 more
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The L$L$‐polynomials of van der Geer–van der Vlugt curves in characteristic 2
Journal of the London Mathematical Society, Volume 113, Issue 3, March 2026.Abstract The van der Geer–van der Vlugt curves form a class of Artin–Schreier coverings of the projective line over finite fields. We provide an explicit formula for their L$L$‐polynomials in characteristic 2, expressed in terms of characters of maximal abelian subgroups of the associated Heisenberg groups.
Tetsushi Ito +2 more
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Nontriviality of rings of integral‐valued polynomials
Mathematische Nachrichten, Volume 298, Issue 12, Page 3974-3994, December 2025.Abstract Let S$S$ be a subset of Z¯$\overline{\mathbb {Z}}$, the ring of all algebraic integers. A polynomial f∈Q[X]$f \in \mathbb {Q}[X]$ is said to be integral‐valued on S$S$ if f(s)∈Z¯$f(s) \in \overline{\mathbb {Z}}$ for all s∈S$s \in S$. The set IntQ(S,Z¯)${\mathrm{Int}}_{\mathbb{Q}}(S,\bar{\mathbb{Z}})$ of all integral‐valued polynomials on S$S ...
Giulio Peruginelli, Nicholas J. Werner
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