Martin's Blog

Functors of points and base ring

Posted by Martin Orr on Thursday, 08 October 2009 at 09:58

So far in my series on functors of points, I have considered functors k\textbf{-Alg} \to \textbf{Set} for some fixed field k. We begin by observing that we may allow k to be any ring. Then I consider whether it is possible to relate functors with base ring k to functors with base ring \mathbb{Z}, with only partial success.

no comments Tags alg-geom, maths, points-func

Morphisms and functors of points

Posted by Martin Orr on Thursday, 01 October 2009 at 15:45

This post will discuss the fact that A-points of an affine k-scheme X (and more general objects) are the same as morphisms \mathop{\mathrm{Spec}_k} A \to X. James already brought this up in his comment last time. As well as proving this in the affine k-scheme case, I shall attempt to give an intuitive explanation of this fact, although I don't find this entirely satisfying.

no comments Tags alg-geom, maths, points-func, yoneda