Le groupe de Selmer des isogénies de hauteur un

2019/04/07 by Damian Rössler, Rössler, Damian
Mathematics · #11G10 #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Meromorphic and Entire Functions #math.AG #msc:11G10

paper · pdf · doi:10.48550/arxiv.1904.03687

in French

arxiv created 2019/04/07 · openalex publication_date 2019/04/07 · arxiv updated 2019/04/09 · openalex created_date 2022/07/29 · openalex updated_date 2026/07/28

Abstract

On montre que le groupe de Selmer d'une isogénie de hauteur un entre deux variétés abéliennes définies sur le corps de fonctions d'une variété quasi-projective et lisse V sur un corps parfait k₀ de caractéristique p>0 peut être plongé dans le groupe des homomorphismes entre deux fibrés vectoriels naturels sur V. / We show that the Selmer group of an isogeny of height one between two abelian varieties defined on the function field of a smooth and quasi-projective variety V over a perfect field k₀ of characteristic p>0 can be embedded in the group of homomorphisms between two natural vector bundles on V.

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• On the group of purely inseparable points of an abelian variety defined over a function field of positive characteristic, II

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