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Zbl 0751.14030
Klapper, A.
Selmer group estimates arising form the existence of canonical subgroups. (English)
[J] Compos. Math. 71, No.2, 121-137 (1989). ISSN 0010-437X; ISSN 1570-5846/e

Author's abstract: 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 $\bbfF\sb p$ ranks of the first flat cohomology groups of these canonical subgroups are found. These results are applied to the estimation of the $\bbfF\sb p$ 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.
[B.Pareigis (München)]

MSC 2000:: *14L05 Formal groups
14K05 Algebraic theory of abelian varieties

Keywords: Frobenius kernel; canonical subgroups of finite height commutative formal groups; local rings; flat cohomology groups; Selmer group of an abelian variety

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Zentralblatt MATH Berlin [Germany]