Catálogo de publicaciones - libros

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 The proof given in [] uses a difficult unpublished ramification-theoretic result of Serre.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.

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 an example of a vector bundle on a relative curve → Spec ℤ such that the restriction to the generic fiber in characteristic zero is semistable but such that the restriction to positive characteristic is not strongly semistable for infinitely many prime numbers . Moreover, under the hypothesis that there exist infinitely many Sophie Germain primes, there are also examples such that the density of primes with nonstrongly semistable reduction is arbitrarily close to one.

Let be a non-isotrivial family of Drinfeld -modules of rank in generic characteristic with a suitable level structure over a connected smooth algebraic variety . Suppose that the endomorphism ring of is equal to . Then we show that the closure of the analytic monodromy group of in SL () is open, where denotes the ring of finite adèles of the quotient field of .

From this we deduce two further results: (1) If is defined over a finitely generated field extension of , the image of the arithmetic étale fundamental group of on the adèlic Tate module of is open in GL (). (2) Let be a Drinfeld -module of rank defined over a finitely generated field extension of , and suppose that cannot be defined over a finite extension of . Suppose again that the endomorphism ring of is . Then the image of the Galois representation on the adèlic Tate module of is open in GL ().

Finally, we extend the above results to the case of arbitrary endomorphism rings.

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.

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.

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 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.

Elliptic sheaves (which are related to Drinfeld modules) were introduced by Drinfeld and further studied by Laumon-Rapoport-Stuhler and others. They can be viewed as function field analogues of elliptic curves and hence are objects “of dimension 1.” Their higher dimensional generalizations are called abelian sheaves. In the analogy between function fields and number fields, abelian sheaves are counterparts of abelian varieties. In this article we study the moduli spaces of abelian sheaves and prove that they are algebraic stacks.We further transfer results of Čerednik-Drinfeld and Rapoport-Zink on the uniformization of Shimura varieties to the setting of abelian sheaves. Actually the analogy of the Čerednik-Drinfeld uniformization is nothing but the uniformization of the moduli schemes of Drinfeld modules by the Drinfeld upper half space. Our results generalize this uniformization. The proof closely follows the ideas of Rapoport-Zink. In particular, analogues of -divisible groups play an important role. As a crucial intermediate step we prove that in a family of abelian sheaves with good reduction at infinity, the set of points where the abelian sheaf is uniformizable in the sense of Anderson, is formally closed.

Let be a non-isotrivial family of Drinfeld -modules of rank in generic characteristic with a suitable level structure over a connected smooth algebraic variety . Suppose that the endomorphism ring of is equal to . Then we show that the closure of the analytic monodromy group of in SL () is open, where denotes the ring of finite adèles of the quotient field of .

From this we deduce two further results: (1) If is defined over a finitely generated field extension of , the image of the arithmetic étale fundamental group of on the adèlic Tate module of is open in GL (). (2) Let be a Drinfeld -module of rank defined over a finitely generated field extension of , and suppose that cannot be defined over a finite extension of . Suppose again that the endomorphism ring of is . Then the image of the Galois representation on the adèlic Tate module of is open in GL ().

Finally, we extend the above results to the case of arbitrary endomorphism rings.