bio | website | preschema.com |
---|---|---|
location | Essen, Germany | |
age | 23 | |
visits | member for | 5 years, 7 months |
seen | Jun 18 at 14:21 | |
stats | profile views | 1,545 |
Apr 6 |
revised |
Integral transform on noncommutative spaces
minor correction |
Apr 6 |
revised |
Integral transform on noncommutative spaces
deleted 17 characters in body |
Apr 6 |
answered | Integral transform on noncommutative spaces |
Apr 5 |
comment |
What is the applications of the dg-enhancements of derived categories of sheaves
@ZhenLin, I notice now that this is made precise, in terms of dg-localization, in section 2.4 of To\"en's notes here. |
Apr 4 |
comment |
What is the applications of the dg-enhancements of derived categories of sheaves
@ZhenLin, this wasn't meant to be a precise statement, but one can probably use the dg-localization or also a spectral analogue instead to make it precise. |
Apr 4 |
answered | What is the applications of the dg-enhancements of derived categories of sheaves |
Apr 1 |
comment |
NCG with all noncommutativity in a nilpotent ideal
In line with Qiaochu's comment, some aspects of E_n-geometry are studied in the thesis of John Francis and this sequel. |
Mar 30 |
comment |
When is the category of small (pre)sheaves a(n elementary) topos?
According to this paper of Mike Shulman, when $\mathcal{P}C$ is finitely complete, it is an infinitary pretopos, so by Giraud's theorem it is a topos iff it admits a small generating set. |
Mar 30 |
answered | Monoidal structure on simplicial sheaves |
Mar 27 |
comment |
Is the derived category of perfect complexes idempotent complete?
In the language of infinity-categories, the relevant result is Proposition 5.5.7.8 in Higher Topos Theory. See also Section 2.4 of arxiv.org/pdf/1001.2282.pdf, especially the text right before Lemma 2.20, for a discussion adapted to the stable setting. |
Mar 27 |
comment |
Is the derived category of perfect complexes idempotent complete?
One good reference is Proposition 2.1.1 here: arxiv.org/abs/math/0204218. |
Mar 25 |
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Do algebraic stacks satisfy fpqc descent?
@Niels, for me an algebraic stack is defined to be a sheaf of groupoids (satisfying some conditions), so I interpret the question as whether or not this sheaf satisfies fpqc descent. |
Mar 25 |
awarded | Explainer |
Mar 25 |
answered | Do algebraic stacks satisfy fpqc descent? |
Mar 25 |
revised |
Do algebraic stacks satisfy fpqc descent?
fix link, which wasn't working |
Mar 25 |
suggested | approved edit on Do algebraic stacks satisfy fpqc descent? |
Mar 23 |
comment |
When do we have $D_{\text{perf}}(\text{Qcoh}(X))\simeq D_{\text{perf}}(X)$?
The functor you write is not an equivalence, but is rather fully faithful with essential image spanned by the complexes with quasi-coherent cohomology. That said, your claim is still true. I doubt that the assumptions can be relaxed, though. Verdier's counterexample in SGA 6 shows that this is unreasonable without something stronger than quasi-separated. While without quasi-compactness, it is not even true that perfect complexes are cohomologically bounded. What kind of generality were you hoping for? |
Mar 13 |
comment |
Brandt's definition of groupoids (1926)
What could you mean by "categories are seen as special $\infty$-groupoids"? |
Mar 12 |
comment |
Choice of fibrations is like a choice of a basis of a module
This is a well-known analogy which I first learned from Chris Schommer-Pries's answer here: mathoverflow.net/a/78408/2503 |
Mar 11 |
comment |
Can motivic E_∞-ring spectra be strictified to commutative motivic symmetric ring spectra?
Note: the proposition cited from Higher Algebra is now numbered 4.5.4.7 in the new version. |