## Selmer group estimates arising form the existence of canonical subgroups.(English)Zbl 0751.14030

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 $$\mathbb{F}_ p$$ ranks of the first flat cohomology groups of these canonical subgroups are found. These results are applied to the estimation of the $$\mathbb{F}_ p$$ 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.

### MSC:

 14L05 Formal groups, $$p$$-divisible groups 14K05 Algebraic theory of abelian varieties
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### References:

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