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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


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.