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pro vyhledávání: '"11G05, 11U05"'
Autor:
Müller, Katharina, Ray, Anwesh
Via a novel application of Iwasawa theory, we study Hilbert's tenth problem for number fields occurring in $\mathbb{Z}_p$-towers of imaginary quadratic fields $K$. For a odd prime $p$, the lines $(a,b) \in \mathbb{P}^1(\mathbb{Z}_p)$ are identified w
Externí odkaz:
http://arxiv.org/abs/2406.01443
Autor:
Ray, Anwesh, Weston, Tom
Let $K$ be a number field and $\ell\geq 5$ be a prime number. Mazur and Rubin introduced the notion of \emph{diophantine stability} for a variety $X_{/K}$ at a prime $\ell$. We show that there is a positive density set of elliptic curves $E_{/\mathbb
Externí odkaz:
http://arxiv.org/abs/2304.09742
We show that Hilbert's Tenth Problem is undecidable for complementary subrings of number fields and that the p-adic and archimedean ring versions of Mazur's conjectures do not hold in these rings. More specifically, given a number field K, a positive
Externí odkaz:
http://arxiv.org/abs/1012.4878
Autor:
Mazur, Barry, Rubin, Karl
In this paper we investigate the 2-Selmer rank in families of quadratic twists of elliptic curves over arbitrary number fields. We give sufficient conditions on an elliptic curve so that it has twists of arbitrary 2-Selmer rank, and we give lower bou
Externí odkaz:
http://arxiv.org/abs/0904.3709
Autor:
Everest, Graham, Eisentraeger, Kirsten
Descent via an isogeny on an elliptic curve is used to construct two subrings of the field of rational numbers, which are complementary in a strong sense, and for which Hilbert's Tenth Problem is undecidable. This method further develops that of Poon
Externí odkaz:
http://arxiv.org/abs/0707.1485
Autor:
Barry Mazur, Karl Rubin
Publikováno v:
Mazur, B.; & Rubin, K.(2010). Ranks of twists of elliptic curves and Hilbert’s tenth problem. Inventiones mathematicae, 181(3), pp 541-575. doi: 10.1007/s00222-010-0252-0. Retrieved from: http://www.escholarship.org/uc/item/3nx8s5vn
In this paper we investigate the 2-Selmer rank in families of quadratic twists of elliptic curves over arbitrary number fields. We give sufficient conditions on an elliptic curve so that it has twists of arbitrary 2-Selmer rank, and we give lower bou
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::9fe7996628841e0bd446660b5a90d24b
http://www.escholarship.org/uc/item/3nx8s5vn
http://www.escholarship.org/uc/item/3nx8s5vn