01. Algebraic geometry - Sheaves (Nickolas Rollick)

Algebraic geometry seminar
Department of Pure Mathematics
University of Waterloo
September 15th, 2016

[emlmm]

A great lecture! That said, if in the future there is a way to have the camera pointed directly at the board rather than at an angle it would be extremely helpful.

[Entropize]

Less interrupting to display vast knowledge and superiority, more interrupting to ask genuine questions and propose clarifications.

[KilgoreTroutAsf]

Nothing like a full board of definitions to begin a topic.

[kodfkdleepd]

Note that one can turn contravariant functors in to covariant with a simple change of wording: Any functor on the open sets with morphisms as inclusion/subset can be converted in to that of a functor who's morphisms are the superset relationship. This flips the direction of the arrows but more importantly shows that it's all about language. We tend to think in terms of subsets rather than super sets and so when we map that concept to other categories the directions may be inverted from what we think(sorta mirror image) because the natural direction, in this example, would be to use supersets rather than subsets.

[LydellAaron]

I remember my calculus teacher at the time, talking about sheaf theory and cohomology and the math you need to get there. 6:04, 23:26

[laflaca]

Beautiful example at the end of the lecture!

[georgediderrich]

Very nice job. I really enjoyed the whole lecture. It cleared up a few things for me.

[AlessandroZir]

thank you very much for making this available to a larger audience! ❤️❤️

[timewasting]

The Lecturer is so patient! omg what's the target audience of this

[kakazpl]

For category, morphisms exist, and compose, but there is no requirement they exists for every pair of objects. For example not every two rings are homomorphic

[rajarshichatterjee]

such a clear ..great series of lectures ..but why ..the camera points at the blackboard from an angle ??? but anyways ..thanks for this informative series of lectures ..very clear lectures ....

[Mll-vh]

It was really help full for me, thank you ....Nickolas Rollick sir

[johnsalkeld]

At 36;10 i think that f-1(W) = Union (f_i)-1(W intersection f_i(Ui)) - i may be wrong as i have never studied sheaves but itfeels like the cover should be involved initially at least

[henrytjernlund]

Due to the bad camera angle I can't see what is being written.

[henrik]

Shouldnt one say that the presheaf is a functor from the opposite category of Open(X) to C? Otherwise one might get the impression that a functor always reverses the order here...

[timelsen]

How is a ring an open set? It's compliment in R is open so a ring is a closed set.

[jeff]

These highly abstract courses being taught with the format of Definition. Theorem. Proof in cycles means the lecturer doesn't really understand the subject itself but are just regurgitating material. It is rare to find an instructor of these courses that truly teach. There is no such thing as teaching, just learning.

[j.rogelioperezbuendia]

comon... a sheaf is a presheaf exactly because you are adding more conditions.

[active]

What an awful blackboard. As expected at least the lower 1/3 is never used, because no-one wants to crawl on the floor half of the time...

[clickaccept]

Good stuff! From the point of view of motivation, it would be very nice to understand, loosely speaking, what the deficiency is with the old concept of variety. Was it simply too restrictive to account for all the examples?