Displaying similar documents to “An equicharacteristic analogue of Hesselholt's conjecture on cohomology of Witt vectors”

Counting discriminants of number fields

Henri Cohen, Francisco Diaz y Diaz, Michel Olivier (2006)

Journal de Théorie des Nombres de Bordeaux

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For each transitive permutation group G on n letters with n ≤ 4 , we give without proof results, conjectures, and numerical computations on discriminants of number fields L of degree n over ℚ such that the Galois group of the Galois closure of L is isomorphic to G .

Random Galois extensions of Hilbertian fields

Lior Bary-Soroker, Arno Fehm (2013)

Journal de Théorie des Nombres de Bordeaux

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Let L be a Galois extension of a countable Hilbertian field K . Although L need not be Hilbertian, we prove that an abundance of large Galois subextensions of L / K are.

When is the order generated by a cubic, quartic or quintic algebraic unit Galois invariant: three conjectures

Stéphane R. Louboutin (2020)

Czechoslovak Mathematical Journal

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Let ε be an algebraic unit of the degree n ≥ 3 . Assume that the extension ℚ ( ε ) / ℚ is Galois. We would like to determine when the order ℤ [ ε ] of ℚ ( ε ) is Gal ( ℚ ( ε ) / ℚ ) -invariant, i.e. when the n complex conjugates ε 1 , ⋯ , ε n of ε are in ℤ [ ε ] , which amounts to asking that ℤ [ ε 1 , ⋯ , ε n ] = ℤ [ ε ] , i.e., that these two orders of ℚ ( ε ) have the same discriminant. This problem has been solved only for n = 3 by using an explicit formula for the discriminant of the order ℤ [ ε 1 , ε 2 , ε 3 ] . However, there is no known similar formula for n > 3 . In the present paper, we put forward and...

Fields of moduli of three-point G -covers with cyclic p -Sylow, II

Andrew Obus (2013)

Journal de Théorie des Nombres de Bordeaux

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We continue the examination of the stable reduction and fields of moduli of G -Galois covers of the projective line over a complete discrete valuation field of mixed characteristic ( 0 , p ) , where G has a p -Sylow subgroup P of order p n . Suppose further that the normalizer of P acts on P via an involution. Under mild assumptions, if f : Y → ℙ 1 is a three-point G -Galois cover defined over ℚ ¯ , then the n th higher ramification groups above p for the upper numbering of the (Galois closure of...

Arithmetic Properties of Generalized Rikuna Polynomials

Z. Chonoles, J. Cullinan, H. Hausman, A.M. Pacelli, S. Pegado, F. Wei (2014)

Publications mathématiques de Besançon

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Fix an integer ℓ ≥ 3 . Rikuna introduced a polynomial r ( x , t ) defined over a function field K ( t ) whose Galois group is cyclic of order ℓ , where K satisfies some mild hypotheses. In this paper we define the family of { r n ( x , t ) } n ≥ 1 of degree ℓ n . The r n ( x , t ) are constructed iteratively from the r ( x , t ) . We compute the Galois groups of the r n ( x , t ) for odd ℓ over an arbitrary base field and give applications to arithmetic dynamical systems.

Piecewise hereditary algebras under field extensions

Jie Li (2021)

Czechoslovak Mathematical Journal

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Let A be a finite-dimensional k -algebra and K / k be a finite separable field extension. We prove that A is derived equivalent to a hereditary algebra if and only if so is A ⊗ k K .