Quotients and equations. (Dans le cadre des rencontres Franco-Colombiennes.)
by Amador Martin-Pizarro (Universität Freiburg)
at Ens Lyon Site Monod ( 4ème étage salle 435 )
Quotients are ubiquitous in Mathematics, and a general question is whether a certain category of sets allows quotients. For the category of definable sets in a given structure, the model theoretic approach is called elimination of imaginaries. For algebraically closed fields, Chevalley’s theorem and the existence of a field of definition of a variety imply that a quotient of a Zariski constructible set by a Zariski constructible equivalence relation is again a constructible set. Similar results hold for other classes of fields, such as differentially closed fields.