Finiteness conditions for finitely generated monoids.
Let be a number field, its ring of integers, and be an irreducible polynomial. Hilbert’s irreducibility theorem gives infinitely many integral specializations such that is still irreducible. In this paper we study the set of those with reducible. We show that is a finite set under rather weak assumptions. In particular, previous results obtained by diophantine approximation techniques, appear as special cases of some of our results. Our method is different. We use elementary group...
We consider deformations of bounded complexes of modules for a profinite group over a field of positive characteristic. We prove a finiteness theorem which provides some sufficient conditions for the versal deformation of such a complex to be represented by a complex of -modules that is strictly perfect over the associated versal deformation ring.
On étudie la notion de finitude géométrique pour certaines géométries de Hilbert définies par un ouvert strictement convexe à bord de classe .La définition dans le cadre des espaces Gromov-hyperboliques fait intervenir l’action du groupe discret considéré sur le bord de l’espace. On montre, en construisant explicitement un contre-exemple, que cette définition doit être renforcée pour obtenir des définitions équivalentes en termes de la géométrie de l’orbifold quotient, similaires à celles obtenues...