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Autour de la conjecture de parité

Abstract : In this thesis, questions related to the parity conjecture are studied. We show the p-parity conjecture for a specific twist of an elliptic curve over a local field. We deduce global results concerning invariance (by some appropriate extensions) of the p-parity conjecture for an elliptic curve. With the objective to expand these results, a formula for root numbers of essentially symplectic and tamely ramified representations of the Weil group is shown. This result generalizes the one already known for elliptic curves with potentially good reduction. Finally, a first step is made toward the generalization on p-parity results whith the comparison of Tamagawa numbers and regulator constants for a premotif (with a few restrictions).
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Contributor : Thomas de la Rochefoucauld <>
Submitted on : Wednesday, October 31, 2012 - 2:26:20 PM
Last modification on : Wednesday, December 9, 2020 - 3:10:33 PM
Long-term archiving on: : Friday, February 1, 2013 - 3:38:28 AM


  • HAL Id : tel-00747423, version 1


Thomas de la Rochefoucauld. Autour de la conjecture de parité. Théorie des nombres [math.NT]. Université Pierre et Marie Curie - Paris VI, 2012. Français. ⟨tel-00747423⟩



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