Aula Seminari - Dipartimento di Matematica
In this seminar I will present some notions of algebraic geometry over subfields introduced and studied in depth in a recent work by Fernando and Ghiloni. I will give an idea of why the most interesting cases to study are those in which the ground field is a real closed field, such as ℝ, and the subfield is not real closed, such as ℚ. We will introduce several notions of real algebraic sets to be `described over ℚ’ and explain some characterizations via Galois theory proved by Fernando-Ghiloni and Ghiloni and the speaker. Time permitting, I will give an insight into which class of algebraic sets `described over ℚ’ is adequate for solving the ℚ-algebrization problem by means of algebraic approximation techniques.