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of 14
pro vyhledávání: '"Jeffrey Hatley"'
Publikováno v:
Transactions of the London Mathematical Society, Vol 6, Iss 1, Pp 22-52 (2019)
Abstract Recently, there has been much interest in studying the torsion subgroups of elliptic curves base‐extended to infinite extensions of Q. In this paper, given a finite group G, we study what happens with the torsion of an elliptic curve E ove
Externí odkaz:
https://doaj.org/article/a750fea942244e84828ebf3f0efab1b2
Autor:
Jeffrey Hatley, Antonio Lei
Publikováno v:
Comptes Rendus. Mathématique. 361:65-72
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::6a4e281567394d844bb71b083a1adb0c
https://doi.org/10.5802/crmath.389
https://doi.org/10.5802/crmath.389
Control theorems for fine Selmer groups, and duality of fine Selmer groups attached to modular forms
Let $\mathcal{O}$ be the ring of integers of a finite extension of $\mathbb{Q}_p$. We prove two control theorems for fine Selmer groups of general cofinitely generated modules over $\mathcal{O}$. We apply these control theorems to compare the fine Se
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::ce5a744de839ecd039f94fc6672be121
Let p be an odd prime and K an imaginary quadratic field where p splits. Under appropriate hypotheses, Bertolini showed that the Selmer group of a p-ordinary elliptic curve over the anticyclotomic $${\mathbb {Z}}_p$$ -extension of K does not admit an
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::df6ec5ba52bd920d6c7b04bb49cb7340
http://hdl.handle.net/11567/1040768
http://hdl.handle.net/11567/1040768
Autor:
Antonio Lei, Jeffrey Hatley
Publikováno v:
Mathematical Research Letters. 26:1115-1144
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::46e2d8c405a3173dd423cea0a4b0b0f1
https://doi.org/10.4310/mrl.2019.v26.n4.a7
https://doi.org/10.4310/mrl.2019.v26.n4.a7
Autor:
Jeffrey Hatley, Antonio Lei
We study the Selmer group associated to a $p$-ordinary newform $f \in S_{2r}(\Gamma_0(N))$ over the anticyclotomic $\mathbb{Z}_p$-extension of an imaginary quadratic field $K/\mathbb{Q}$. Under certain assumptions, we prove that this Selmer group has
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::d69ac4c7b51163ce439e25f153f13d18
Publikováno v:
Transactions of the London Mathematical Society, Vol 6, Iss 1, Pp 22-52 (2019)
Recently there has been much interest in studying the torsion subgroups of elliptic curves base-extended to infinite extensions of $\mathbb{Q}$. In this paper, given a finite group $G$, we study what happens with the torsion of an elliptic curve $E$
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::8849ed2aa1b248ab237bdb79f99cfab7
http://arxiv.org/abs/1803.09614
http://arxiv.org/abs/1803.09614
Autor:
Jeffrey Hatley, Antonio Lei
We extend many results on Selmer groups for elliptic curves and modular forms to the non-ordinary setting. More precisely, we study the signed Selmer groups defined using the machinery of Wach modules over $\mathbf{Z}_p$-cyclotomic extensions. First,
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::7746485a89824d970f107770dac95a7a
http://arxiv.org/abs/1608.00257
http://arxiv.org/abs/1608.00257
Autor:
Jeffrey Hatley
A result of Dieulefait-Wiese proves the existence of modular eigenforms of weight 2 for which the image of every associated residual Galois representation is as large as possible. We generalize this result to eigenforms of general even weight k $\geq
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::2d3fda46245335d587981f22481ea1a5
http://arxiv.org/abs/1601.02863
http://arxiv.org/abs/1601.02863
Autor:
Jeffrey Hatley
A recent paper of Shekhar compares the ranks of elliptic curves $E_1$ and $E_2$ for which there is an isomorphism $E_1[p] \simeq E_2[p]$ as $\mathrm{Gal}(\bar{\mathbf{Q}}/\mathbf{Q})$-modules, where $p$ is a prime of good ordinary reduction for both
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::cd724dee58938fc432ba5b2329203213