Simone Ramello (Università di Torino): Étale methods in the model theory of fields
Thursday, 06.05.2021 10:30 im Raum via Zoom
Introduced by Johnson, Tran, Walsberg and Ye, the so-called étale-open topology effectively acts as a dictionary between the topological and the algebraic worlds; in particular, algebraic properties of a field an be characterized as topological properties of the étale-open topology on the affine line, and moreover the étale-open topology turns out to be the "usual suspects" when considered over certain classes of fields -- the Zariski topology on separably closed fields, the order topology on real closed fields... The étale-open topology also allows to characterize large fields, as introduced by Pop in 1996, precisely as the class of fields over which it is not the discrete topology. This allows to turn a statement like the stable fields conjecture into an almost purely topological question, at least in the large case, and eventually leads to proving the conjecture in this scenario.