The first purpose of schemes theory is the geometrical study of solutions of algebraic systems of equations, not only over the real/complex numbers, but also over integer numbers (and more generally over any commutative ring with 1).It was finalized by Alexandre GROTHENDIECK, during the 1950's and ...
Someone recently asked what the epimorphisms in the category of schemes are; the other day I had been wondering about the similar question: what are the monomorphisms in the category of schemes? I am ...
Many people seem to know the following. Personally, I don't quite understand it though and maybe I'm wrong. It's the fact that "a vector bundle on an open subscheme extends in only one way to a vector ...
Is there an example of a variety over the complex numbers with no embedding into a smooth variety?
Wellpowered means that for every scheme $X$, the subobject lattice of monormophisms $Y \to X$ is essentially small; regularly wellpowered means that for every scheme $X$, the regular subobject lattice ...
Let $S$ be a scheme. We consider the functor, called affine hull, from the category of quasicompact and quasiseparated $S$-schemes to the category of affine $S$-schemes, defined as a left adjoint to ...
Let $f: X \to Y$ be a morphism of schemes over a field $k$ such that $f$ induces (1) a bijection between their closed points, and (2) an isomorphism of their Zariski tangent spaces. Under these ...