Seminario Teoría de Grupos ICMAT-UAM

Jueves 20 de Junio, 11:30 Aula 520, UAM

Adrien Deloro (Institut de Mathématiques de Jussieu,  Sorbonne Université)

Título: Linearisation in model theory, revisited (joint with F. Wagner)

Resumen: "Three years ago, I gave here a seminar with the same title. And yet... this will be a completely different (and of course independent) talk on the same topic: new setting, new result, new methods.

To linearise is to retrieve a (skew-)field structure; Schur's Lemma in representation theory is the basic observation that the set of endomorphisms of a given irreducible representation forms a field. But to linearise in model theory means to find a field definable in first-order logic, something completely not obvious from Schur's construction.

The first result on definability of the Schur field was by Boris Zilber in the seventies, in a very specific model-theoretic context.

We try to provide the ultimate generalisation of the Schur-Zilber "definable field theorem", in the new model-theoretic setting of finite-dimensional theories (which will be discussed)."