Isogenies of elliptic curves and the Morava stabilizer group

Mark Behrens, Tyler Lawson

Research output: Contribution to journalArticle

9 Scopus citations

Abstract

Let S2 be the p-primary second Morava stabilizer group, C a supersingular elliptic curve over over(F, -)p, O the ring of endomorphisms of C, and ℓ a topological generator of Zp× (or Z2× / {± 1} if p = 2). We show that for p > 2 the group Γ ⊆ O [1 / ℓ]× of quasi-endomorphisms of degree a power of ℓ is dense in S2. For p = 2, we show that Γ is dense in an index 2 subgroup of S2.

Original languageEnglish (US)
Pages (from-to)37-49
Number of pages13
JournalJournal of Pure and Applied Algebra
Volume207
Issue number1
DOIs
StatePublished - Sep 1 2006
Externally publishedYes

Keywords

  • Morava stabilizer group
  • Quaternion algebras
  • Supersingular elliptic curves

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