Iwasawa theory of elliptic curves at supersingular primes over ℤ p -extensions of number fields

By A. Iovita, Robert H. Pollack. 2004

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Abstract In this paper, we make a study of the Iwasawa theory of an elliptic curve at a supersingular prime p along an arbitrary ℤp-extension of a number field K in the case when p splits completely in K. Generalizing work of Kobayashi [S. Kobayashi, Iwasawa theory for elliptic curves at supersingular primes, Invent. Math. 152 (2003), no. 1, 1–36.] and Perrin-Riou [B. Perrin-Riou, Arithmétique des courbes elliptiques á réduction supersingulière en p, Experiment. Math. 12 (2003), no. 2, 155–186.], we define restricted Selmer groups and λ±, μ±-invariants; we then derive asymptotic formulas describing the growth of the Selmer group in terms of these invariants. To be able to work with non-cyclotomic ℤ p -extensions, a new local result is proven that gives a complete description of the formal group of an elliptic curve at a supersingular prime along any ramified ℤ p -extension of ℚ p .

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

View Paper: https://www.semanticscholar.org/paper/c3d24339285ae5b95b31a8998e34da0cbac3f6d9

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In Algebra and Number Theory

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

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 replaces H(1) ord(K∞,w, Af ) with the plus/minus local condition of [24, 20].”