Iwasawa theory for elliptic curves at supersingular primes: A pair of main conjectures

JOURNAL OF NUMBER THEORY

卷:132

Article

关键词: Elliptic curves;    Iwasawa theory;    Supersingular primes;   

DOI  :  10.1016/j.jnt.2011.11.003

来源: Elsevier

【 摘 要 】

Text. We extend Kobayashi's formulation of Iwasawa theory for elliptic curves at supersingular primes to include the case a(p) not equal 0, where a(p) is the trace of Frobenius. To do this, we algebraically construct p-adic L-functions L-p(#) and L-p(b) with the good growth properties of the classical Pollack p-adic L-functions that in fact match them exactly when ap = 0 and p is odd. We then generalize Kobayashi's methods to define two Selmer groups Sel(#) and Sel(b) 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(b). We then use results by Kato to prove a divisibility statement. Video. For a video summary of this paper, please click here a: visit http://www.youtube.com/watch?v=Y7gPQsBZo6s. (C) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

Free