Isogenies of elliptic curves and the Morava stabilizer group

Details Isogenies of elliptic curves and the Morava stabilizer group Isogenies of elliptic curves and the Morava stabilizer group

2005-08-03

arxiv.org/abs/math/0508079v1

Mathematics

Algebraic Topology

16 pages, to appear in J. Pure Appl. Alg

Scientific paper

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 \Gamma \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 \Gamma is dense in an index 2 subgroup of MS_2.

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