Catálogo de publicaciones - libros

We describe a tautological subring in the arithmetic Chow ring of bases of abelian schemes. Among the results are an Arakelov version of the Hirzebruch proportionality principle and a formula for a critical power of ĉ of the Hodge bundle.

We study the basic height conjecture for points on curves defined over number fields and show: On any algebraic curve defined over a number field the set of algebraic points contains an unrestricted subset of infinite cardinality such that for all of its points their canonical height is bounded in terms of a small power of their root discriminant. In addition, if we assume GRH, then the upper bound is, as it is conjectured, linear in the logarithm of the root discriminant.

This paper introduces a novel architecture to efficiently code in a self-organized manner, data from sequences or a hierarchy of sequences. The main objective of the architecture proposed is to achieve an inductive model of the sequential data through a learning algorithm in a finite vector space with generalization and prediction properties improved by the compression process. The architecture consists of a hierarchy of recurrent self-organized maps with emergence which performs a fractal codification of the sequences. An adaptive outlier detection algorithm is used to automatically extract the emergent properties of the maps. A visualization technique to help the analysis and interpretation of data is also developed. Experiments and results for the architecture are shown for an anomaly intrusion detection problem.

We give a new proof of the fact that the even terms (of a multiple of) the Chern character of the Hodge bundles of semi-abelian schemes are torsion classes in Chow theory and we give explicit bounds for almost all the prime powers appearing in their order. These bounds appear in the numerators of modified Bernoulli numbers. We also obtain similar results in an equivariant situation.

In [], R. Pink and the author gave a short proof of the Manin-Mumford conjecture, which was inspired by an earlier model-theoretic proof by Hrushovski. The proof given in [] uses a difficult unpublished ramification-theoretic result of Serre. It is the purpose of this note to show how the proof given in [] can be modified so as to circumvent the reference to Serre’s result. J. Oesterlé and R. Pink contributed several simplifications and shortcuts to this note.