Affine Varieties and Schemes

[@danielpfeffer2473]

Looks like youtube mislabeled your section on Hilbert's Nullstellensatz. Great video!

Hey Daniel, great video! :-) At 13:50 the important thing why Grothendieck used prime ideals is not that he wanted to go more general but its because max Ideals are just not the right object. mSpec wont be a functor in that case.

[@lalaskustabaskus9026]

Wow just stumbled on this by accident. Please keep up this great work. You can be the more advanced (older brother) version of Wildbergers Math channel! Keep posting videos!!!

[@NoNTr1v1aL]

Amazing video!

[@robinbalean958]

Very nice lecture!

[@mactorresmo]

Fabulous teachings! Thanks Daniel!

[@levkruglyak]

What a fantastic lecture. Thank you very much

[@douggwyn9656]

Audio needs boosting.

[@gidi5779]

Great video! Thank you very much!

[@lelandreardon7844]

A bit subtle at ~18:00. We're talking about "closed points" of Spec(Z), but we're determining if they're closed as subspaces of Z under the Zariski Topology? Nevertheless they're merely points in Spec(Z), correct? I.e. they're trivially closed sets of Spec(Z), but that's not the point being made?

[@DanielChanMaths]

Some points are not closed. The prime ideal 0 in particular, is not closed in Spec (Z) since it is not of the form V(I) for some ideal I. The closure of the singleton set {0} is actually the whole of Spec(Z)!

[@EdwinSteiner]

Very good explanation! Thank you!