Riv. Mat. Univ. Parma, Vol. 7, No. 1, 2016

Luca Demangos[1]

A few remarks on a Manin-Mumford conjecture in function field arithmetic and generalized Pila-Wilkie estimates

Pages: 205-216
Received: 29 December 2015
Accepted in revised form: 17 February 2016
Mathematics Subject Classification (2010): 11G09, 14G22.
Keywords: \(T-\)modules, rational points, Manin-Mumford conjecture, local fields.
Author address:
[1] : Universidad Nacional Autonoma de Mexico, Av. Universidad S/N, C.P. 62210, Cuernavaca, Morelos, MEXICO

Abstract: We present here the natural extension of our Pila-Wilkie type estimates on the number of rational points of the trascendent part of a compact analytic subset of \(\mathbb{F}_{q}((1/T))^{n}\) (see [D1]) to analogous subsets of \(K^{n}\), where \(K\) is a general local field of any characteristic. That would integrate the analogous estimate provided by F. Loeser, G. Comte and R. Cluckers in [CCL, Theorem 4.1.6]. We remind in the first two sections the main ideas of our construction by correcting two minor mistakes we made in [D1]. We then generalize the strategy to any local field.


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