Displaying similar documents to “Subfields of the function field of the Deligne-Lusztig curve of Ree type”

Extending automorphisms to the rational fractions field.

Fernando Fernández Rodríguez, Agustín Llerena Achutegui (1991)

Extracta Mathematicae

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We say that a field K has the Extension Property if every automorphism of K(X) extends to an automorphism of K. J.M. Gamboa and T. Recio [2] have introduced this concept, naive in appearance, because of its crucial role in the study of homogeneity conditions in spaces of orderings of functions fields. Gamboa [1] has studied several classes of fields with this property: Algebraic extensions of the field Q of rational numbers; euclidean, algebraically closed and pythagorean fields; fields...

On the ordinarity of the maximal real subfield of cyclotomic function fields

Daisuke Shiomi (2014)

Acta Arithmetica

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The aim of this paper is to clarify the ordinarity of cyclotomic function fields. In the previous work [J. Number Theory 133 (2013)], the author determined all monic irreducible polynomials m such that the maximal real subfield of the mth cyclotomic function field is ordinary. In this paper, we extend this result to the general case.

Properties of extensions of algebraically maximal fields.

G. Leloup (2003)

Collectanea Mathematica

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We prove some properties similar to the theorem Ax-Kochen-Ershov, in some cases of pairs of algebraically maximal fields of residue characteristic p > 0. This properties hold in particular for pairs of Kaplansky fields of equal characteristic, formally p-adic fields and finitely ramified fields. From that we derive results about decidability of such extensions.

Class numbers of totally real fields and applications to the Weber class number problem

John C. Miller (2014)

Acta Arithmetica

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The determination of the class number of totally real fields of large discriminant is known to be a difficult problem. The Minkowski bound is too large to be useful, and the root discriminant of the field can be too large to be treated by Odlyzko's discriminant bounds. We describe a new technique for determining the class number of such fields, allowing us to attack the class number problem for a large class of number fields not treatable by previously known methods. We give an application...