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11528
bio website preschema.com
location Essen, Germany
age 23
visits member for 5 years, 7 months
seen Jun 18 at 14:21

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
comment 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.