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Homotopy theory, homological algebra, algebraic treatments of manifolds.

4 votes
Accepted

Does there exist a classification of covering spaces in algebraic geometry?

Yes, (and of course): The very definition of the étale fundamental group is that it classifies finite étale covers. Precisely: Let $X$ be a connected scheme and $x$ be a geometric point of $X$. There …
Xandi Tuni's user avatar
  • 4,015
5 votes
2 answers
450 views

Which $H$--groups satisfy the rigidity property of abelian varieties?

Let us call a group object $G$ in a category $\mathcal C$ rigid, if it has the following property: For every group object $X$ in $\mathcal C$, every morphism $G\to X$ in $\mathcal C$ respecting the u …
Xandi Tuni's user avatar
  • 4,015