Iwasawa theory for elliptic curves at supersingular primes

By Shin-ichi Kobayashi. 2003

261 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/b51f66ae5cd27d9fe1b7b391f70d210ad25bab5b

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In Algebra and Number Theory

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Iwasawa Main Conjecture for Supersingular Elliptic Curves (2014, methodology): “1≤m≤n,2∤m Φm(X) (our definition is slightly different from [9]).”
The p-adic Gross-Zagier formula for elliptic curves at supersingular primes (2013, unknown): “このような局所点の族は Perrin‐Riou map の構成や [19], [11] で本質的な役割を果たしている.”
On anticyclotomic μ-invariants of modular forms (2006, background): “If f is a p-supersingular modular form, then the above discussion goes through if for each place w of K∞ dividing p one replacesH 1 ord(K∞,w, Af ) with the plus/minus local condition of [24, 20].”
Iwasawa theory for modular forms at supersingular primes (2009, methodology): “Using the notation from section 2, for all n ≥ 0, as in [7], we define the even and odd Selmer groups by”
The main conjecture for CM elliptic curves at supersingular primes (2005, background): “Proof. The first two assertions are Proposition 8.12(ii) of [ Ko ].”
On the p-adic L-function of a modular form at a supersingular prime (2003, background): “Kobayashi in [10] has constructed two restricted Selmer groups sitting inside the full Selmer group of E over Q∞ which are torsion over the Iwasawa algebra.”
Iwasawa theory for elliptic curves at supersingular primes: A pair of main conjectures (2009, methodology): “ a certain sum, e.g. forp odd, Lp(E,α,X) = L+ p(E,X)log+ p(1 + X) + L− p(E,X)log− p(1 + X)α, where L± p ∈Zp[[X]]. Kobayashi then constructed two Zp[[X]]-cotorsion subgroups of the Selmer group Sel±in [Kobayashi] and formulated a pair of Iwasawa main conjectures in the spirit of Mazur’s ordinary one:”