More than over any field, over any ring. For example, that allows you to look at families of curves or talk about reduction modulo p (if you do number theory) v

More than over any field, over any ring. For example, that allows you to look at families of curves or talk about reduction modulo p (if you do number theory) very nicely/naturally. A mathoverflow thread with cool uses of schemes: https://mathoverflow.net/questions/59071/what-elementary-problems-can-you-solve-with-schemes?answertab=votes#tab-top https://mathoverflow.net/questions/59071/what-elementary-pro...