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- W1750276513 abstract "Let A be a complex abelian variety and G its Mumford--Tate group. Supposing that the simple abelian subvarieties of A are pairwise non-isogenous, we find a lower bound for the rank of G, which is a little less than log_2 dim A. If we suppose that End A is commutative, then we show that rk G >= log_2 dim A + 2, and this latter bound is sharp. We also obtain the same results for the rank of the l-adic monodromy group of an abelian variety defined over a number field. ----- Soit A une vari'et'e ab'elienne complexe et G son groupe de Mumford--Tate. En supposant que les sous vari'et'es ab'eliennes simples de A sont deux `a deux non-isog`enes, on trouve une minoration du rang rk G de G, l'eg`erement inf'erieure `a log_2 dim A. Si on suppose que End A est commutatif, alors on montre que rk G >= log_2 dim A + 2, et cette borne-ci est optimale. On obtient les m^emes resultats pour le rang du groupe de monodromie l-adique d'une vari'et'e ab'elienne d'efinie sur un corps de nombres." @default.
- W1750276513 created "2016-06-24" @default.
- W1750276513 creator A5004407401 @default.
- W1750276513 date "2011-10-31" @default.
- W1750276513 modified "2023-09-27" @default.
- W1750276513 title "Lower bounds for ranks of Mumford-Tate groups" @default.
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