All Questions
Tagged with derived-algebraic-geometry homotopy-theory
7 questions
35
votes
2
answers
3k
views
What is the relationship between connective and nonconnective derived algebraic geometry?
"Derived algebraic geometry" usually means the study of geometry locally modeled on "$Spec R$" where $R$ is a connective $E_\infty$ ring spectrum (perhaps with further restrictions). Why "connective", ...
- 64k
21
votes
1
answer
3k
views
Motivation and potential applications of spectral algebraic geometry
Nowadays there is a lot of talk about derived algebraic geometry, but not so much about the related subject of spectral algebraic geometry.
Now I'm curious what future is there for spectral algebraic ...
- 433
44
votes
5
answers
6k
views
What is the cotangent complex good for?
The cotangent complex seems to be a pretty fundamental object in algebraic geometry, but if it's treated in Hartshorne then I missed it. It seems to be even more important in derived algebraic ...
- 64k
23
votes
2
answers
2k
views
Why do people say DG-algebras behave badly in positive characteristic?
It seems to be a common wisdom in derived algebraic geometry that commutative DG-algebras are not, in general, a good model for derived rings, with the stated reason that they behave badly in positive ...
- 231
11
votes
1
answer
650
views
Thom Spectra and Hopf-Galois Extensions of Ring Spectra
So I've been fiddling with this for a long time, so apologies to anyone that's already heard me talk about this ad nauseum. I haven't been able to get anywhere with it, and it seemed that as such, it ...
- 10.5k
10
votes
1
answer
883
views
$\infty$-categorical understanding of Bridgeland stability?
On triangulated categories we have a notion of Bridgeland stability conditions.
Is there any known notion of "derived stability conditions" on a stable $\infty$-category $C$ such that they become ...
- 103
5
votes
1
answer
298
views
Interpolating between the flat and smooth affine lines in spectral algebraic geometry
Consider the following construction (which came up recently in a question about "spectral exterior algebras"):
Pick a ring spectrum $R$ and consider the $\infty$-category $\mathsf{Mod}_R$ ...
- 11.8k