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arXiv · 0807.0171

Une minoration du minimum essentiel sur les varietes abeliennes

Aurelien Galateau
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Abstract

We extend to the general codimension a lower bound for the essential minimum on abelian varieties found in a previous work, under a conjecture about ordinary primes in abelian varieties. This lower bound is the best expected, ``up to an epsilon'', in the degree of the subvariety. Following a strategy of Amoroso, we change the transcendance phasis in order to simplify the zero lemma and its combinatorics. The last argument is a descent procedure on varieties, which is far more intricate in the abelian setting since there is not, in general, a lifting of the Frobenius in characteristic zero.

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Aurelien Galateau. 2008-07-01. Une minoration du minimum essentiel sur les varietes abeliennes. https://arxiv.org/abs/0807.0171

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