Mathematics – Number Theory
Scientific paper
2009-03-19
Mathematics
Number Theory
26 pages. Basically a new article. Has been expanded and revised incorporating comments made by the referee and many others
Scientific paper
We extend Kobayashi's formulation of Iwasawa theory for elliptic curves at supersingular primes to include the case $a_p \neq 0$, where $a_p$ is the trace of Frobenius. To do this, we algebraically construct $p$-adic $L$-functions $L_p^{\sharp}$ and $L_p^{\flat}$ 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 $\Sel^{\sharp}$ and $\Sel^{\flat}$ 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 $L_p^{\sharp}$ and $L_p^{\flat}$. We then use results by Kato to prove a divisibility statement.
No associations
LandOfFree
Iwasawa theory for elliptic curves at supersingular primes: A pair of main conjectures does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Iwasawa theory for elliptic curves at supersingular primes: A pair of main conjectures, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Iwasawa theory for elliptic curves at supersingular primes: A pair of main conjectures will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-641380