bio  website  preschema.com 

location  Essen, Germany  
age  23  
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1d

comment 
is there a moduli of stable infinity categories?
@pro, thanks. I know that moduli stacks of dgcategories are discussed in To\"en's beautiful paper on derived Azumaya algebras, which has been generalized to a spectral stack parametrizing Rlinear categories for R a commutative ring spectrum by AntieauGepner. I don't think they discuss the type of issue you are interested in there, though. 
1d

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Homotopy pullback preserving functor
@FernandoMuro, I may be missing something, but if $A$ and $B$ have the trivial model structures, then the condition of preserving fibrations and weak equivalences is vacuous, while the condition of preserving homotopy fibres is a type of leftexactness, right? 
1d

comment 
Homotopy pullback preserving functor
@FernandoMuro, the proposition in the paper says that the functor preserves fibrations in the model structure, not fibre sequences. 
1d

comment 
is there a moduli of stable infinity categories?
@pro, thanks! Would you mind also sharing the approximations that you found in the literature? 
1d

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is there a moduli of stable infinity categories?
@pro, would you mind explaining what you mean by infinitesimal theory here? 
Apr 28 
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Is there any explicit result on the triangulated category of singularities of a curve?
Do you know a reference for that? I only knew that fact in the smooth case. 
Apr 28 
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Is there any explicit result on the triangulated category of singularities of a curve?
Just a comment: a semiorthogonal decomposition of D^b_coh induces a semiorthogonal decomposition of D_sg, according to Corollary 1.12 here. 
Apr 22 
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Are Bökstedt's THH manuscripts available?
I could email them to you. 
Apr 9 
comment 
Algebraic Ktheory of complex varieties
Analytic descent for Ktheory would follow directly from analytic descent for perfect complexes. I have no idea whether the latter is true, though. 
Apr 6 
comment 
Integral transform on noncommutative spaces
@bananastack, I learned this from Marco Robalo's thesis, but it is probably in some paper of To\"en. 
Apr 6 
comment 
How does one compute a colimit of monoidal categories?
I believe nonstrict monoidal categories can be described as algebras over a monad which is a cofibrant replacement of the monad presenting strict monoidal categories. So a similar statement should hold. 
Apr 6 
comment 
Integral transform on noncommutative spaces
@bananastack, saturated dgcategories also come from dgalgebras, by the way (from dgalgebras of finite type, even). 
Apr 5 
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What is the applications of the dgenhancements of derived categories of sheaves
@ZhenLin, I notice now that this is made precise, in terms of dglocalization, in section 2.4 of To\"en's notes here. 
Apr 4 
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What is the applications of the dgenhancements of derived categories of sheaves
@ZhenLin, this wasn't meant to be a precise statement, but one can probably use the dglocalization or also a spectral analogue instead to make it precise. 
Apr 1 
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NCG with all noncommutativity in a nilpotent ideal
In line with Qiaochu's comment, some aspects of E_ngeometry are studied in the thesis of John Francis and this sequel. 
Mar 30 
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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 27 
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Is the derived category of perfect complexes idempotent complete?
In the language of infinitycategories, 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 
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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 23 
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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 quasicoherent 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 quasiseparated. While without quasicompactness, it is not even true that perfect complexes are cohomologically bounded. What kind of generality were you hoping for? 