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"correct official definition" is that a morphism of varieties is a morphism of "ringed spaces" underlying varieties (which is actually missing and I'm going...

It might be nice to have a couple of examples of algebraic varieties in order to make these ideas more concrete and easier to understand. ConfusedGremlin...

section, it is stated that correspondences generalize morphisms of algebraic varieties X → Y. It is also claimed a little below that there is a functor...

regular maps is to have everything in algebraic geometry as local polynomial maps, and ultimately as algebraic varieties, I imagine to use then polynomial...

the (unique) morphism from X to Spec Z is smooth. A scheme X over another scheme S is called "smooth over S" if the structure morphism X → S is smooth...

this article defines "isogeny" by "an isogeny is a morphism of varieties between two abelian varieties (e.g. elliptic curves) that is surjective and has...

essentially a stub for algebraic stacks, i.e., very particular types of stacks in groupoids that are suitably "covered" by algebraic spaces. Whereas stacks...

describing the intersections of algebraic curves.", but this is not sourced... Here is a source which writes that algebraic geometry was ingurated with...

I have started writing up a section for defining the gysin morphism... The Gysin morphism i ! : A d ( Y ) → A d − r ( X ) {\displaystyle i^{!}:A_{d}(Y)\to...

one-one morphism from A onto B; an automorphism is an isomorphism of an algebra with itself, and an endomorphism is a morphism of an algebra into itself...

Mention degeneration theorems Include examples Smooth morphism of varieties Quotient varieties + equivariant cohomology (http://www.ams...

satisfactory). An algebraic variety X is separated if the diagonal in X x X is a closed subset. Affine varieties as well as projective varieties are separated...

projective varieties contains Pm×Pn. If you like, the issue is not what the product is, but where it is. The Segre embedding is strictly a morphism, not an...

call an "algebraic theory" is a category whose internal language is capable of expressing an algebraic theory. Category theorists have a habit of re-defining...

invariants of Hilbert scheme of K3 and generalized Kummer. -- Tiphareth 05:25, 26 December 2006 (UTC) "Birational morphism" is a morphism which is defined...

K-rational points on algebraic varieties" reads: "The Weil conjectures concern the distribution of rational points on varieties over finite fields." Once...

surprised if it really works well for an arbitrary morphism; I would only expect it to work for a morphism satisfying some conditions (like being a locally...

example of universal morphism. It says that ( X × Y , π 1 × π 2 ) {\displaystyle (X\times Y,\pi _{1}\times \pi _{2})} is a universal morphism for ( X...

Discussion on flat morphisms: Flat morphism is linked in the preceding section. Explaining "the geometric intuition for flat morphisms of schemes" belongs...

"Localization of categories". The (category of) abelian varieties up to isogeny etc. should be treated as examples, then. I have not seen abelian varieties up to...