Differential Field Arithmetic

Abstract: I will discuss some of my upcoming thesis work under the supervision of Anand Pillay. Some of this work is also joint with Omar León Sánchez. Motivated by existence questions in differential Galois theory, I will discuss our recent efforts to generalize a theorem of Serre from the algebraic to the differential algebraic setting. Serre's theorem states: A field F is bounded (has finitely many extensions of each finite degree) if and only if the first Galois cohomology set with coefficients in any linear algebraic group defined over F is trivial. This talk will emphasize our development of basic computational tools for definable Galois cohomology, a model theoretic generalization of (differential) algebraic Galois cohomology. All of the relevant notions will be introduced, including some background on differential Galois theory.

logicnumber theory

Audience: researchers in the topic

Online logic seminar

Series comments: Description: Seminar on all areas of logic