arXiv subjects

Amador Martin-Pizarro

Publications and source records attributed to Amador Martin-Pizarro.

23 records · Page 2Linked to original sources

arXiv2014

De Beaux Groupes

In this short paper, we will provide a characterisation of interpretable groups in a beautiful pair (K, E) of algebraically closed fields : every interpretable group is, up to isogeny, the extension of the subgroup of E-rational points of an algebraic group by an interpretable group which is the quotient of an algebraic group by the E-rational points of an algebraic subgroup.---Dans une belle paire (K;E) de corps algébriquement clos, un groupe définissable se projette, à isogénie près, sur les points E-rationnels d'un groupe algébrique ayant pour noyau un groupe algébrique. Un groupe interprétable est, à isogénie près, l'extension des points E-rationnels d'un groupe algébrique par un groupe interprétable, qui est lui le quotient d'un groupe algébrique par les points E-rationnels d'un sous-groupe algébrique.

math.LO↗

arXiv2013

Ample Hierarchy

The ample hierarchy of geometries of stables theories is strict. We generalise the construction of the free pseudospace to higher dimensions and show that the n-dimensional free pseudospace is ω-stable n-ample yet not (n+1)-ample. In particular, the free pseudospace is not 3-ample. A thorough study of forking is conducted and an explicit description of canonical bases is exhibited.

math.LO↗

arXiv2012

On Variants of CM-triviality

We introduce a generalization of CM-triviality relative to a fixed invariant collection of partial types, in analogy to the Canonical Base Property defined by Pillay, Ziegler and Chatzidakis which generalizes one-basedness. We show that, under this condition, a stable field is internal to the family, and a group of finite Lascar rank has a normal nilpotent subgroup such that the quotient is almost internal to the family.

math.LO↗

arXiv2011

Generic points on exponential curves

We show, assuming Schanuel's conjecture, that every irreducible complex polynomial in two variables where both variables appear has infinitely many algebraically independent solutions of the form (z,e^z).

math.NT↗

arXiv2006

On fields and colours

We exhibit a simplified version of the construction of a field of Morley rank p with a predicate of rank p-1, extracting the main ideas for the construction from previous papers and refining the arguments. Moreover, an explicit axiomatization is given, and ranks are computed.

math.LO↗