TY - JOUR
T1 - Iwasawa theory for elliptic curves at supersingular primes
T2 - A pair of main conjectures
AU - Sprung, Florian E.Ito
N1 - Copyright:
Copyright 2012 Elsevier B.V., All rights reserved.
PY - 2012/7
Y1 - 2012/7
N2 - Text: We extend Kobayashi's formulation of Iwasawa theory for elliptic curves at supersingular primes to include the case a p≠0, where a p is the trace of Frobenius. To do this, we algebraically construct p-adic L-functions L p # and L p ≠ with the good growth properties of the classical Pollack p-adic L-functions that in fact match them exactly when a p=0 and p is odd. We then generalize Kobayashi's methods to define two Selmer groups Sel # and Sel ≠ and formulate a main conjecture, stating that each characteristic ideal of the duals of these Selmer groups is generated by our p-adic L-functions L p # and L p ≠. We then use results by Kato to prove a divisibility statement. Video: For a video summary of this paper, please click here or visit http://www.youtube.com/watch?v=Y7gPQsBZo6s.
AB - Text: We extend Kobayashi's formulation of Iwasawa theory for elliptic curves at supersingular primes to include the case a p≠0, where a p is the trace of Frobenius. To do this, we algebraically construct p-adic L-functions L p # and L p ≠ with the good growth properties of the classical Pollack p-adic L-functions that in fact match them exactly when a p=0 and p is odd. We then generalize Kobayashi's methods to define two Selmer groups Sel # and Sel ≠ and formulate a main conjecture, stating that each characteristic ideal of the duals of these Selmer groups is generated by our p-adic L-functions L p # and L p ≠. We then use results by Kato to prove a divisibility statement. Video: For a video summary of this paper, please click here or visit http://www.youtube.com/watch?v=Y7gPQsBZo6s.
KW - Elliptic curves
KW - Iwasawa theory
KW - Supersingular primes
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U2 - 10.1016/j.jnt.2011.11.003
DO - 10.1016/j.jnt.2011.11.003
M3 - Article
AN - SCOPUS:84857683335
VL - 132
SP - 1483
EP - 1506
JO - Journal of Number Theory
JF - Journal of Number Theory
SN - 0022-314X
IS - 7
ER -