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7 votes
0 answers
574 views

What is the geometric intuition for the sheaf-theoretic terms "soft", "fine", and "flabby"?

The sheaf-theoretic terms "soft", "flabby", and "fine" are of an obviously geometric character, and suggest opposition with "hard", "rigid", and "coarse" sheaves (I'm just inventing these terms here). ...
13 votes
1 answer
1k views

How is a Stack the generalisation of a sheaf from a 2-category point of view?

A stack is usually given in terms of: -A category $F$ fibered over another $C$ such that the functor $Hom(x,y), x,y \in F(\alpha), \alpha \in C$ is a sheaf -The descent data are effective. There ...
13 votes
1 answer
583 views

Which nice/deep elaborations on the (operators <-> sheaves) / (endomorphisms <-> objects) theme are there?

A linear operator $T:V\to V$ on a (say) vector space over a field $k$ is just a $k[T]$-module, and may be viewed as the sheaf $\mathscr F_T$ over $\mathbb A^1_k$, with fibre over $\lambda\in k$ equal ...
16 votes
4 answers
2k views

Coboundaries and Gluing in Cech Cohomology - Intuition?

I'm trying to develop an intuition for Cech cohomology geometrically, but am currently failing. A lot of people seem to say that the groups $H^n$ measure obstructions to gluing local sections to get ...
11 votes
3 answers
6k views

Serre's FAC versus Hartshorne as an introduction to sheaves in algebraic geometry

I just found an English translation of Serre's FAC at Richard Borcherds' Algebraic Geometry course web page. I really want to read it sometime. I am beginner in Algebraic Geometry, just started ...