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bio website preschema.com
location Essen, Germany
age 23
visits member for 5 years, 5 months
seen 49 mins ago

1d
comment is there a moduli of stable infinity categories?
@pro, thanks. I know that moduli stacks of dg-categories are discussed in To\"en's beautiful paper on derived Azumaya algebras, which has been generalized to a spectral stack parametrizing R-linear categories for R a commutative ring spectrum by Antieau-Gepner. I don't think they discuss the type of issue you are interested in there, though.
1d
comment 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 left-exactness, 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
comment is there a moduli of stable infinity categories?
@pro, would you mind explaining what you mean by infinitesimal theory here?
Apr
28
comment 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
comment Is there any explicit result on the triangulated category of singularities of a curve?
Just a comment: a semi-orthogonal decomposition of D^b_coh induces a semi-orthogonal decomposition of D_sg, according to Corollary 1.12 here.
Apr
22
comment Are Bökstedt's THH manuscripts available?
I could e-mail them to you.
Apr
9
comment Algebraic K-theory of complex varieties
Analytic descent for K-theory 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 non-strict 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 dg-categories also come from dg-algebras, by the way (from dg-algebras of finite type, even).
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
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
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
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?