Post #1506852

@cbaberle Excellent post summarizing a ton of work! (I have to admit I was a little nervous there would be no credit assigned —except to Ingo Blechschmidt, Felix Cherubini, Thierry Coquand, Matthias Hutzler, David Wärn, Hugo Moeneclaey— until I got to the end where all the references are! 😅) One thing I noticed was wrong is this sentence: "For commutative rings A, B the homomorphisms A → B are in natural bijection with continuous maps Spec(B) → Spec(A)." This is very far from true! Take A = B = Z, for example. There is a unique ring homomorphism A → B but there are uncountably many continuous functions Spec(B) → Spec(A): fix 0 and permute the primes however you want amongst themselves. One nearby correct statement is, of course, that you can equip the topological space Spec(A) with the structure of a scheme and then ring homomorphisms A → B are in natural bijection with morphisms of schemes Spec(B) → Spec(A).