Rubin’s conjecture on local units in the anticyclotomic tower at inert primes
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This article is published in Annals of Mathematics.The article was published on 2021-11-01 and is currently open access. It has received 3 citations till now. The article focuses on the topics: Tower (mathematics) & Iwasawa theory.read more
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The even parity Goldfeld conjecture: Congruent number elliptic curves
TL;DR: In this paper , the congruent number elliptic curves have been studied in the context of the first instance of Goldfeld's conjecture, where 50% of the quadratic twists of an elliptic curve defined over rationals have analytic rank zero.
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Supersingular elliptic curves over ℤ𝑝-extensions
TL;DR: In this article , the structure of the points E (L ∞ ) \mathrm{E}(L_{\infty}) and the global implications of the results were analyzed.
References
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Book
Elementary and analytic theory of algebraic numbers
TL;DR: In this paper, Dedekind Domains and Valuations have been used to define the theory of P-adic fields and to define a local compact Abelian group. But they do not consider the relation between the two types of fields.
Book
Arithmetic moduli of elliptic curves
Nicholas M. Katz,Barry Mazur +1 more
TL;DR: A comprehensive treatment of recent developments in the study of elliptic curves and their moduli spaces is given in this article, including the work of Deligne and Drinfeld, and a complete account of that progress is given.
Book
Primes of the Form x2 + ny2: Fermat, Class Field Theory, and Complex Multiplication
Abstract: FROM FERMAT TO GAUSS. Fermat, Euler and Quadratic Reciprocity. Lagrange, Legendre and Quadratic Forms. Gauss, Composition and Genera. Cubic and Biquadratic Reciprocity. CLASS FIELD THEORY. The Hilbert Class Field and p = x 2 + ny 2 . The Hilbert Class Field and Genus Theory. Orders in Imaginary Quadratic Fields. Class Fields Theory and the Cebotarev Density Theorem. Ring Class Field and p = x 2 + ny 2 . COMPLEX MULTIPLICATION. Elliptic Functions and Complex Multiplication. Modular Functions and Ring Class Fields. Modular Functions and Singular j--Invariants. The Class Equation. Ellpitic Curves. References. Index.
Journal ArticleDOI
Iwasawa theory for elliptic curves at supersingular primes
TL;DR: In this article, a new formulation in Iwasawa theory for elliptic curves at good supersingular primes was given, which is similar to Mazur's at good ordinary primes.
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Anticyclotomic p-ordinary Iwasawa theory of elliptic modular forms
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