Iwasawa Main Conjecture for Supersingular Elliptic Curves

By X. Wan. 2014

61 citations recorded by the source corpus.

In this paper we prove the $\pm$-main conjecture formulated by Kobayashi for elliptic curves with supersingular reduction at $p$ such that $a_p=0$, using a new idea of reducing it to another Iwasawa-Greenberg main conjecture, which is more accessible and proved here as a first step. Then we develop some generalized $\pm$ local theory and deduce the main conjecture. The argument uses in an essential way the recent study on explicit reciprocity law for Beilinson-Flach elements by Kings-Loeffler-Zerbes. We also prove as corollaries the $p$-part of the BSD formula at supersingular primes when the analytic rank is $0$ or $1$.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/226d8e641a217649bd3e4addc42cb4ea6cf9fdac

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In Discrete Mathematics and Combinatorics

1. C. Skinner
2. Dimitar Jetchev
3. X. Wan

In Geometry and Topology

1. X. Wan
2. Dimitar Jetchev
3. C. Skinner
4. Wei Zhang

In Mathematical Physics

1. X. Wan
2. Dimitar Jetchev
3. C. Skinner
4. Wei Zhang

Citations in the corpus

• The Birch and Swinnerton-Dyer Formula for Elliptic Curves of Analytic Rank One (2015, methodology): “C] as a consequence of the proof Iwasawa main conjecture for GL2, and that of part (iii) for the supersingular case is a consequence of the proof of Kobayashi’s main conjecture [Wan14b, Cor.4.8].”