Date:
Thu, 04/01/202414:30-15:30
Location:
Manchester, Hall 2
Title: Models of elliptic curves, using model theory
Abstract: Given a valued field (K,v) with valuation ring O and an algebraic group G over K, a model of G is a group scheme \mathcal{G} over O for which \mathcal{G} \times_O K=G. We exhibit the existence of such models for G an elliptic curve and K an algebraically closed field, and on the way we classify the different group schemes one can get. The proof uses a combination of tools from model theory and algebraic geometry.
The aim of this talk is to state the theorem and to introduce some of the model-theoretic notions required for the proof.
No prior knowledge of model theory is required, though a basic course in logic will help.
Panopto Link: https://huji.cloud.panopto.eu/Panopto/Pages/Viewer.aspx?id=613f85ff-4467-4e55-8737-b0d7006d9003
Abstract: Given a valued field (K,v) with valuation ring O and an algebraic group G over K, a model of G is a group scheme \mathcal{G} over O for which \mathcal{G} \times_O K=G. We exhibit the existence of such models for G an elliptic curve and K an algebraically closed field, and on the way we classify the different group schemes one can get. The proof uses a combination of tools from model theory and algebraic geometry.
The aim of this talk is to state the theorem and to introduce some of the model-theoretic notions required for the proof.
No prior knowledge of model theory is required, though a basic course in logic will help.
Panopto Link: https://huji.cloud.panopto.eu/Panopto/Pages/Viewer.aspx?id=613f85ff-4467-4e55-8737-b0d7006d9003