Operads, Strings and Deligne's Conjecture

10.1142/6641 ◽  
2014 ◽  
Author(s):  
Ralph M Kaufmann
Keyword(s):  
Deligne's Conjecture

scholarly journals CyclicA∞structures and Deligne’s conjecture

2012 ◽  
Vol 12 (3) ◽  
pp. 1487-1551 ◽  
Author(s):  
Benjamin C Ward
Keyword(s):  
Deligne's Conjecture

scholarly journals Algebraicity of L-values for elliptic curves in a false Tate curve tower

2007 ◽  
Vol 142 (2) ◽  
pp. 193-204 ◽  
Author(s):  
THANASIS BOUGANIS ◽  
VLADIMIR DOKCHITSER
Keyword(s):  
Elliptic Curve ◽  
Elliptic Curves ◽  
Abelian Extension ◽  
Deligne's Conjecture ◽  
Special Value ◽  
Positive Integers ◽  
Tate Curve

AbstractLet E be an elliptic curve over ${\mathbb Q}$, and τ an Artin representation over ${\mathbb Q}$ that factors through the non-abelian extension ${\mathbb Q}(\sqrt[p^n]{m},\mu_{p^n})/{\mathbb Q}$, where p is an odd prime and n, m are positive integers. We show that L(E,τ,1), the special value at s=1 of the L-function of the twist of E by τ, divided by the classical transcendental period Ω+d+|Ω−d−|ε(τ) is algebraic and Galois-equivariant, as predicted by Deligne's conjecture.

scholarly journals Operadic twisting – With an application to Deligne's conjecture

2015 ◽  
Vol 219 (5) ◽  
pp. 1349-1428 ◽  
Author(s):  
Vasily Dolgushev ◽  
Thomas Willwacher
Keyword(s):  
Deligne's Conjecture
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