Grothendieck's Schemes in Algebraic Geometry

Anthony Bordg, Lawrence C. Paulson and Wenda Li

29 March 2021


We formalize mainstream structures in algebraic geometry culminating in Grothendieck's schemes: presheaves of rings, sheaves of rings, ringed spaces, locally ringed spaces, affine schemes and schemes. We prove that the spectrum of a ring is a locally ringed space, hence an affine scheme. Finally, we prove that any affine scheme is a scheme.
BSD License

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