Displaying similar documents to “On Bilinear Structures on Divisor Class Groups”

The period-index problem in WC-groups IV: a local transition theorem

Pete L. Clark (2010)

Journal de Théorie des Nombres de Bordeaux

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Let K be a complete discretely valued field with perfect residue field k . Assuming upper bounds on the relation between period and index for WC-groups over k , we deduce corresponding upper bounds on the relation between period and index for WC-groups over K . Up to a constant depending only on the dimension of the torsor, we recover theorems of Lichtenbaum and Milne in a “duality free” context. Our techniques include the use of of torsors under abelian varieties with good reduction and...

On elementary equivalence, isomorphism and isogeny

Pete L. Clark (2006)

Journal de Théorie des Nombres de Bordeaux

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Motivated by recent work of Florian Pop, we study the connections between three notions of equivalence of function fields: isomorphism, elementary equivalence, and the condition that each of a pair of fields can be embedded in the other, which we call isogeny. Some of our results are purely geometric: we give an isogeny classification of Severi-Brauer varieties and quadric surfaces. These results are applied to deduce new instances of “elementary equivalence implies isomorphism”: for...

Non-existence and splitting theorems for normal integral bases

Cornelius Greither, Henri Johnston (2012)

Annales de l’institut Fourier

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We establish new conditions that prevent the existence of (weak) normal integral bases in tame Galois extensions of number fields. This leads to the following result: under appropriate technical hypotheses, the existence of a normal integral basis in the upper layer of an abelian tower ℚ ⊂ K ⊂ L forces the tower to be split in a very strong sense.

Galois Covers and the Hilbert-Grunwald Property

Pierre Dèbes, Nour Ghazi (2012)

Annales de l’institut Fourier

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Our main result combines three topics: it contains a Grunwald-Wang type conclusion, a version of Hilbert’s irreducibility theorem and a p -adic form à la Harbater, but with good reduction, of the Regular Inverse Galois Problem. As a consequence we obtain a statement that questions the RIGP over ℚ . The general strategy is to study and exploit the good reduction of certain twisted models of the covers and of the associated moduli spaces.

Selmer groups for elliptic curves in ℤ l d -extensions of function fields of characteristic p

Andrea Bandini, Ignazio Longhi (2009)

Annales de l’institut Fourier

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Let F be a function field of characteristic p > 0 , ℱ / F a ℤ l d -extension (for some prime l ≠ p ) and E / F a non-isotrivial elliptic curve. We study the behaviour of the r -parts of the Selmer groups ( r any prime) in the subextensions of ℱ via appropriate versions of Mazur’s Control Theorem. As a consequence we prove that the limit of the Selmer groups is a cofinitely generated (in some cases cotorsion) module over the Iwasawa algebra of ℱ / F .