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On local root numbers of abelian varieties

Abstract : The aim of this thesis is to produce a formula for the local root number of an abelian variety defined over a p-adic field in terms of some other invariants. If A has real multiplication, then it must have either potentially good or potentially toric reduction. In the former case we give formulas of the local root number under the condition that the inertia action on the 1st étale cohomology group is abelian, in the latter the root number depends only on the type of the Néron model. In the next part we consider the Jacobian of a 5-adic curve of genus 2 such that the inertia action is wild and maximal. We prove a few criteria to identify this setting. Our initial formula for the root number of J depends on a particular Weierstrass equation E. Using this equation, we show a formula for the Tamagawa number of J. This allows to express the root number of J independently of E.
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Contributor : Lukas Melninkas <>
Submitted on : Wednesday, July 7, 2021 - 2:17:45 PM
Last modification on : Thursday, July 8, 2021 - 3:37:55 AM


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  • HAL Id : tel-03258699, version 2



Lukas Melninkas. On local root numbers of abelian varieties. Number Theory [math.NT]. Université de Strasbourg, 2021. English. ⟨tel-03258699v2⟩



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