The Witt ring of an elliptic curve over a local field

1996 ◽  
Vol 306 (1) ◽  
pp. 391-418 ◽  
Author(s):  
J�n Kr. Arason ◽  
Richard Elman ◽  
Bill Jacob
Keyword(s):  
Elliptic Curve ◽  
Local Field ◽  
Witt Ring

scholarly journals The Witt ring of a curve with good reduction over a non-dyadic local field

2015 ◽  
Vol 422 ◽  
pp. 648-659 ◽  
Author(s):  
Jeanne M. Funk ◽  
Raymond T. Hoobler
Keyword(s):  
Local Field ◽  
Good Reduction ◽  
Witt Ring

scholarly journals The remaining cases of the Kramer–Tunnell conjecture

2016 ◽  
Vol 152 (11) ◽  
pp. 2255-2268
Author(s):  
Kęstutis Česnavičius ◽  
Naoki Imai
Keyword(s):  
Elliptic Curve ◽  
Local Field ◽  
Positive Characteristic ◽  
Quadratic Extension ◽  
Base Change ◽  
Local Fields ◽  
Root Number ◽  
Characteristic Case ◽  
Local Root

For an elliptic curve $E$ over a local field $K$ and a separable quadratic extension of $K$, motivated by connections to the Birch and Swinnerton-Dyer conjecture, Kramer and Tunnell have conjectured a formula for computing the local root number of the base change of $E$ to the quadratic extension in terms of a certain norm index. The formula is known in all cases except some where $K$ is of characteristic $2$, and we complete its proof by reducing the positive characteristic case to characteristic $0$. For this reduction, we exploit the principle that local fields of characteristic $p$ can be approximated by finite extensions of $\mathbb{Q}_{p}$: we find an elliptic curve $E^{\prime }$ defined over a $p$-adic field such that all the terms in the Kramer–Tunnell formula for $E^{\prime }$ are equal to those for $E$.

scholarly journals Optimal Quotients of Jacobians With Toric Reduction and Component Groups

2016 ◽  
Vol 68 (6) ◽  
pp. 1362-1381
Author(s):  
Mihran Papikian ◽  
Joseph Rabinoff
Keyword(s):  
Elliptic Curve ◽  
Local Field ◽  
Modular Curves ◽  
Jacobian Variety ◽  
Neron Models ◽  
Néron Models

AbstractLet J be a Jacobian variety with toric reduction over a local field K. Let J → E be an optimal quotient defined over K, where E is an elliptic curve. We give examples in which the functorially induced map on component groups of the Néron models is not surjective. This answers a question of Ribet and Takahashi. We also give various criteria under which is surjective and discuss when these criteria hold for the Jacobians of modular curves.

Vagus Nerve Stimulation Induced Synchrony Modulation of Local Field Potential in the Rat Cerebral Cortex

2013 ◽  
Vol 133 (8) ◽  
pp. 1493-1500 ◽  
Author(s):  
Ryuji Kano ◽  
Kenichi Usami ◽  
Takahiro Noda ◽  
Tomoyo I. Shiramatsu ◽  
Ryohei Kanzaki ◽  
...  
Keyword(s):  
Cerebral Cortex ◽  
Vagus Nerve ◽  
Local Field ◽  
Nerve Stimulation ◽  
Local Field Potential ◽  
Vagus Nerve Stimulation ◽  
Field Potential ◽  
Rat Cerebral Cortex

Study of Safe Elliptic Curve Cryptography over Gaussian Integer

2020 ◽  
Vol E103.A (12) ◽  
pp. 1624-1628
Author(s):  
Kazuki NAGANUMA ◽  
Takashi SUZUKI ◽  
Hiroyuki TSUJI ◽  
Tomoaki KIMURA
Keyword(s):  
Elliptic Curve ◽  
Elliptic Curve Cryptography ◽  
Gaussian Integer
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