9
votes
1answer
420 views

Why is there no stack of $\ell$-adic sheaves on a curve?

One of the main players in the categorical geometric langlands correspondence is the moduli stack of rank n integrable connections on a complex curve. The reason for considering such objects is that ...
4
votes
1answer
275 views

fpqc sheafification and localisation

I am slightly confused about sheafification at the moment. I first learned sheaves defined as a subcategory of presheaves, then I was told that sheaves are also a localisation of presheaves, then I ...
5
votes
1answer
1k views

surjective morphism of schemes or epimorphism of sheaves?

I have a technical question coming from reading Toen's master course on stacks. If we view schemes as locally ringed spaces then there we could define a morphism to be surjective if it the underlying ...