Blvd Garibaldi : Variations sur Yona Friedman

Variations sur l'effet Condorcet

Skip Garibaldi and Detlev

In a 2004 paper, Totaro asked whether a G-torsor X that has a zero-cycle of degree d > 0 will necessarily have a closed étale point of degree dividing d, where G is a connected algebraic group. This question is closely related to several conjectures regarding exceptional algebraic groups. Totaro gave a positive answer to his question in the following cases: G simple, split, and of type G2, type...

Sara Friedman

Variations sur le théorème de Cassels, Ellison et Pfister

Artin [Ar] (1927) : Une fraction rationnelle f ∈ R(X1, . . . , Xn) positive sur R est une somme de carrés. Pfister [Pf] (1967) : c’est une somme de 2 carrés. En particulier pour n = 2, f ∈ 4 R(X,Y ). Cassels, Ellison, Pfister [CEP] (1971) : 4 carrés sont vraiment nécéssaires (i.e. le nombre de Pythagore de R(X, Y ) est 4, car le polynôme de Motzkin 1 + XY 4 + XY 2 − 3XY , positif ou nul, ne s’é...

Variations sur un THème de Aldama et Shelah

We study the definability of certain subgroups of a group G that does not have the independence property. If a (type) definable subset X of an elementary extension G of G has property P , we call its trace X∩G over G an externally (type) definable P set. We show the following. Centralisers of subsets of G are externally definable subgroups. Cores of externally definable subgroups and iterated c...