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. 
BibTeX: 
@article{Grothendieck_SchemesAFP,
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{https://isaafp.org/entries/Grothendieck_Schemes.html},
Formal proof development},
ISSN = {2150914x},
}
