Grothendieck's Schemes in Algebraic Geometry


Title: Grothendieck's Schemes in Algebraic Geometry
Authors: Anthony Bordg, Lawrence Paulson and Wenda Li
Submission date: 2021-03-29
Abstract: 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.
  author  = {Anthony Bordg and Lawrence Paulson and Wenda Li},
  title   = {Grothendieck's Schemes in Algebraic Geometry},
  journal = {Archive of Formal Proofs},
  month   = mar,
  year    = 2021,
  note    = {\url{},
            Formal proof development},
  ISSN    = {2150-914x},
License: BSD License
Depends on: Jacobson_Basic_Algebra
Status: [ok] This is a development version of this entry. It might change over time and is not stable. Please refer to release versions for citations.