Indivisibility of class numbers of global function fields
Allison M. Pacelli, Michael Rosen (2009)
Acta Arithmetica
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Allison M. Pacelli, Michael Rosen (2009)
Acta Arithmetica
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Angus Macintyre (1971)
Fundamenta Mathematicae
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Attila Pethő, Michael E. Pohst (2012)
Acta Arithmetica
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Paulo Ribenboim (1984)
Rendiconti del Seminario Matematico della Università di Padova
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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.
Jan-Hendrik Evertse (1986)
Acta Arithmetica
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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...
V. Sprindžuk (1974)
Acta Arithmetica
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Dress, Andreas W.M. (1997)
Beiträge zur Algebra und Geometrie
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Eiji Yoshida (2003)
Acta Arithmetica
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Jack Ohm (1989)
Journal de théorie des nombres de Bordeaux
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Some results and problems that arise in connection with the foundations of the theory of ruled and rational field extensions are discussed.