arXiv subjects

Alberto Angurel

Publications and source records attributed to Alberto Angurel.

2 recordsLinked to original sources

arXiv2026

Ultra Kolyvagin systems and higher Fitting ideals of Iwasawa Selmer groups

We develop the theory of equivariant, ultra Kolyvagin systems to bypass structural limitations of the Euler system machinery over infinite rings. By utilizing collections of classes living in the exterior powers of patched Selmer groups -- constructed from ultraproducts of classical Selmer groups -- we compute the structure of an Iwasawa Selmer group up to pseudo-isomorphism of Iwasawa modules and prove the absence of finite submodules. We apply this theoretical framework to the fine Selmer group of an elliptic curve and the Bloch-Kato Selmer group of the Rankin-Selberg convolution of modular forms.

math.NT↗

arXiv2025

Kolyvagin systems of rank 0 and the structure of the Selmer group of elliptic curves over abelian extensions

With the motivation to study the Selmer group of an elliptic curve, we improve the theory of Kolyvagin systems to describe the Fitting ideals of a Selmer group in the core rank zero situation. By relaxing a Selmer structure of rank zero at certain prime, we can construct an auxiliary Kolyvagin system whose localisation determines most of the Fitting ideals of the Selmer group, and all of them when the Galois representation is not self-dual. With this new theory, one can describe, in terms of the modular symbols, the Galois structure of the Selmer group of an elliptic curve $E/\mathbb{Q}$ over a finite abelian extension whose degree is coprime to $p$.

math.NT↗