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Abstract: In this article we give explicit formulae for a lift of the relativeFrobenius morphism between elliptic curves and show how one can compute thislift in the case of ordinary reduction in odd characteristic. Our theory canalso be used in the case of supersingular reduction. By means of the explicitformulae that describe a Frobenius lift, we are able to generalize Mestre-s2-adic arithmetic geometric mean AGM sequence of elliptic curves to oddcharacteristic, and prove its convergence. As an application, we give anefficient point counting algorithm for ordinary elliptic curves which is basedon the generalized AGM sequence.



Author: Robert Carls

Source: https://arxiv.org/







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