All Questions
Tagged with derived-algebraic-geometry ring-spectra
9 questions
2
votes
0
answers
116
views
Quasicompact quasiaffine classical schemes are nonconnectively-affine
In this answer to What is the relationship between connective and nonconnective derived algebraic geometry? I learned that any quasicompact open subscheme of an affine scheme is affine in the sense of ...
- 448
2
votes
1
answer
173
views
Monoidal colimit-preserving functor from spaces to $A$-modules
I am reading Lurie's Elliptic Cohomology II and it claims (Section 4.1.3) that for an $\mathbb{E}_\infty$-ring $A$ "there is an essentially unique symmetric monoidal functor $\mathcal{S} \to \...
4
votes
0
answers
153
views
Preorientation of additive formal group
In "A Survey of Elliptic Cohomology", Section 3.2, Lurie asserts that the preorientations of the additive formal group $\widehat{\mathbf G}_a$ over $\mathbf Z$ are classified by the $\mathbb ...
- 2,011
5
votes
1
answer
321
views
Is there a definition of reduced $E_\infty$ ring?
[Edit: I have completely changed the question in response to the replies given]
I am curious if there is well defined notion of reduced $E_\infty$-ring.
Let $CAlg$ denote the $\infty$-category of $E_\...
- 448
4
votes
0
answers
477
views
DAG applied to homotopy theory: how to reach research level?
It is my dream to do research on applications of spectral algebraic geometry in homotopy theory one day. Specifically, giving a more uniform treatment for the results proved via scary computations (of ...
19
votes
1
answer
1k
views
A sheaf is a presheaf that preserves small limits
There is a common misconception that a sheaf is simply a presheaf that preserves limits. This has been discussed here before many times and I believe I understand it well enough.
However when reading ...
15
votes
0
answers
3k
views
What to expect from spectral algebraic geometry
So I've been trying to learn some derived algebraic geometry, and I've chosen to approach the subject from the perspective of spectral or "brave new" algebraic geometry. Without having to go through ...
- 3,019
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
14
votes
0
answers
930
views
$E_{\infty}$ $R$-algebras vs commutative DG $R$-algebras vs simplicial commutative $R$-algebras
I've been trying to understand better the relation between the basic blocks of derived algebraic geometry. More precisely, I'm trying to understand the relation between the DG approach, the spectral ...
- 2,227