Is there any equivalence between the category of schemes over $\mathbb R$ and the category real manifolds
The equivalence of the category of smooth projective curves over $\mathbb C$ and the category of compact Riemann surfaces is, I believe, well documented. For example, it is mentioned on the wiki page: ...
I am just beginning to learn scheme theory. This question is aimed at getting a feel for something so apologies in advance for the lack of precision. I am struck by the following difference from the ...
Some questions about schemes and varieties, one really basic. I follow the definitions as given in Hartshorne. Firstly, my main question. I understood that Grothendiecks introduction of schemes ...
In algebraic geometry one (mostly) studies varieties given by polynomial equations. Such equations define algebraic varieties and there are many "dictionaries" available. For example, the category ...
This question may be a little bit metaphysical:are there any important properties about the generic points on a scheme?Or rather,why do we introduce the concept of generic point?I am not very clear ...