All Questions

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 ...

What is sheaf cohomology intuitively? For local systems it is ordinary cohomology with twisted coefficients. But what if the sheaf in question is far from being constant? Can one still understand ...

Once in a while I run into literature that invokes vanishing cycle machinery with a cryptic sentence like, "this follows from a standard vanishing cycle argument." Is there a good way to look at ...

We know that presheaves of any category have enough projectives and that sheaves do not, why is this, and how does it effect our thinking? This question was asked(and I found it very helpful) but I ...

I find the definition for locales and sheaves on locales to be straightforward, but I'm stumbling over the idea of a Grothendieck topology. Is there a nice way to see roughly how the latter ...