Isogenies of elliptic curves and the Morava stabilizer group

Mark Behrens; Tyler Lawson

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Isogenies of elliptic curves and the Morava stabilizer group

Mark Behrens·Tyler Lawson

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Abstract

Let MS_2 be the p-primary second Morava stabilizer group, C a supersingular elliptic curve over \br{FF}_p, O the ring of endomorphisms of C, and \ell a topological generator of Z_p^x (respectively Z_2^x/{+-1} if p = 2). We show that for p > 2 the group Γ\subseteq O[1/\ell]^x of quasi-endomorphisms of degree a power of \ell is dense in MS_2. For p = 2, we show that Γis dense in an index 2 subgroup of MS_2.

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BibTeX RIS

Mark Behrens, Tyler Lawson. 2005-08-03. Isogenies of elliptic curves and the Morava stabilizer group. https://arxiv.org/abs/math/0508079

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