Thursday 19th of October 2023, 13:30-14:30 in LIN8
Finn Bartsch
Algebraic curves and their function fields.
Algebraic geometry is fundamentally about studying the shape of zero sets of polynomials in multiple variables. One of the main recurring themes in this area of mathematics is the interplay between "geometric" objects (like a curve or a surface) and "algebraic" objects (like a ring or a field). We illustrate this interplay by looking at one of the simplest possible shapes, that of a curve. There we see that the theory of a certain class of curves, namely the "smooth projective" ones, can be described in a purely field-theoretic manner.