# Max Zeuner: Geometric and functorial schemes from the constructive predicative viewpoint

**Time: **
Wed 2023-06-14 10.00 - 12.00

**Location: **
Albano house 1, floor 3, Room U (Kovalevsky)

**Participating: **
Max Zeuner, Stockholm University

### Abstract

Schemes are usually defined using locally ringed spaces but for algebraic geometers it can be more convenient to work with the functor of points associated to a scheme. In fact, Grothendieck favored the approach of defining schemes directly as certain well-behaved functors from rings to sets. These "functorial schemes" are easily shown equivalent to the "geometric schemes" defined through locally ringed spaces. I this talk we look at how much of this picture can be recovered when working constructively and predicatively.