Results 171 to 180 of about 4,471 (200)

Elliptic Curves with Supersingular Reduction over $��$-extensions

2012
This is a translation of a research announcement by Anas G. Nasybullin from 1976, in which he states formulas for the p-primary part of the Tate-Shafarevich group of an elliptic curve in cyclotomic $\Z_p$-extensions of number fields.
Minevich, Igor, Sprung, Florian
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A supersingularity criterion of elliptic curves

Journal of Mathematical Sciences, 1997
A well-known Belyi theorem states that an arbitrary algebraic curve defined over \(\overline \mathbb{Q}\) can be mapped onto the projective line \(\mathbb{P}^1\) so that the whole of ramification will be concentrated over three points of \(\mathbb{P}^1\) (we may assume that these points are \(\infty, 0,1)\).
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On the Iwasawa $\mu $-invariants of supersingular elliptic curves

Acta Arithmetica, 2020
This paper considers elliptic curves \(E\) and certain torsion Iwasawa modules attached to \(E\) and a fixed odd prime \(p\). Let \(X(E)\) be the dual of the \(p\)-Selmer group of \(E\) over the \(p\)-cyclotomic extension \(\mathbb Q_\infty/\mathbb Q\). In previous work with \textit{R. Barman} [Bull. Braz. Math. Soc. (N.S.) 41, No.
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Supersingular Elliptic Curves in Cryptography

2007
I will survey the checkered history of supersingular elliptic curves in cryptography, from their first consideration in the seminal papers of Koblitz and Miller, to their rejection after the discovery of the Weil and Tate pairing attacks on the discrete logarithm problem for these curves, and concluding with their resurrection alongside the discovery ...
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On the supersingular reduction of elliptic curves

Proceedings of the Indian Academy of Sciences - Section A, 1987
Let E be an elliptic curve over \({\mathbb{Q}}\), and let p be a prime of supersingular reduction for E. The author shows that the 2-complement of \(E({\mathbb{F}}_ p)\) is cyclic. In particular, if \(E_ a\) is the curve \(y^ 2=(x^ 2+1)(x+a)\) (a\(\in {\mathbb{Q}})\) the author combines the above result with Elkies' theorem (that there are infinitely ...
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Iwasawa theory for elliptic curves at supersingular primes

Inventiones Mathematicae, 2003
Let \(p\) be an odd prime, \({\mathbb Q}_{\infty} = \bigcup_{n}\;F_{n}\) the cyclotomic \({\mathbb Z}_{p}\)-extension of \({\mathbb Q},\) \(\wedge\) the usual Iwasawa algebra. In the Iwasawa theory of elliptic curves at good ordinary primes, the Main Conjecture states that the Selmer group over \({\mathbb Q}_{\infty}\) is \(\wedge\)-cotorsion and the ...
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Attributes and predictors of long COVID

Nature Medicine, 2021
Carole H Sudre, Benjamin Murray, Thomas Varsavsky   +2 more
exaly  

The role of adsorbed hydroxide in hydrogen evolution reaction kinetics on modified platinum

Nature Energy, 2020
Ian T Mccrum, Marc T M Koper
exaly  

The IntCal20 Northern Hemisphere Radiocarbon Age Calibration Curve (0–55 cal kBP)

Radiocarbon, 2020
Paula J Reimer, Alex Bayliss, Paul G Blackwell   +2 more
exaly  

A reflective, metal-rich atmosphere for GJ 1214b from its JWST phase curve

Nature, 2023
Eliza M-R Kempton, Michael Zhang, Maria E Steinrueck   +2 more
exaly