Selmer Group Estimates Arising from the Existence of Canonical Subgroups
نویسنده
چکیده
Generalizing the work of Lubin in the one dimensional case, conditions are found for the existence of canonical subgroups of finite height commutative formal groups of arbitrary dimension over local rings of mixed characteristic (0, p). These are p-torsion subgroups which are optimally close to being kernels of Frobenius homomorphisms. The Fp ranks of the first flat cohomology groups of these canonical subgroups are found. These results are applied to the estimation of the Fp rank of the Selmer group of an Abelian variety over a global number field of characteristic zero, and the lim sup of these ranks as the Abelian variety varies in an isogeny class.
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