Geodesic
The main conjecture for ${\rm CM}$ elliptic curves at supersingular primes
Robert Pollack1 ; Karl Rubin2
1 Department of Mathematics, University of Chicago, Chicago, IL 60637, United States
2 Department of Mathematics, Stanford University, Stanford, CA 94305, United States
Annals of mathematics, Tome 159 (2004) no. 1, pp. 447-464

Voir la notice de l'article provenant de la source Annals of Mathematics website

At a prime of ordinary reduction, the Iwasawa “main conjecture” for elliptic curves relates a Selmer group to a $p$-adic $L$-function. In the supersingular case, the statement of the main conjecture is more complicated as neither the Selmer group nor the $p$-adic $L$-function is well-behaved. Recently Kobayashi discovered an equivalent formulation of the main conjecture at supersingular primes that is similar in structure to the ordinary case. Namely, Kobayashi’s conjecture relates modified Selmer groups, which he defined, with modified $p$-adic $L$-functions defined by the first author. In this paper we prove Kobayashi’s conjecture for elliptic curves with complex multiplication.

DOI : 10.4007/annals.2004.159.447

Robert Pollack 1 ; Karl Rubin 2

1 Department of Mathematics, University of Chicago, Chicago, IL 60637, United States
2 Department of Mathematics, Stanford University, Stanford, CA 94305, United States 
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Robert Pollack; Karl Rubin. The main conjecture for ${\rm CM}$ elliptic curves at supersingular primes. Annals of mathematics, Tome 159 (2004) no. 1, pp. 447-464. doi: 10.4007/annals.2004.159.447

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