Displaying similar documents to “On counterexamples to local-global divisibility in commutative algebraic groups”

On second 2-descent and non-congruent numbers

Yi Ouyang, Shenxing Zhang (2015)

Acta Arithmetica

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We use the so-called second 2-descent method to find several series of non-congruent numbers. We consider three different 2-isogenies of the congruent elliptic curves and their duals, and find a necessary condition to estimate the size of the images of the 2-Selmer groups in the Selmer groups of the isogeny.

Finite-dimensional differential algebraic groups and the Picard-Vessiot theory

Anand Pillay (2002)

Banach Center Publications

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We make some observations relating the theory of finite-dimensional differential algebraic groups (the ∂₀-groups of [2]) to the Galois theory of linear differential equations. Given a differential field (K,∂), we exhibit a surjective functor from (absolutely) split (in the sense of Buium) ∂₀-groups G over K to Picard-Vessiot extensions L of K, such that G is K-split iff L = K. In fact we give a generalization to "K-good" ∂₀-groups. We also point out that the "Katz group" (a certain linear...