bio  website  preschema.com 

location  Essen, Germany  
age  23  
visits  member for  5 years, 4 months 
seen  37 mins ago  
stats  profile views  1,454 
9h

answered  Could we extend the exact sequence $K^0(X)\to K_0(X)\to K_0(D_{sg}(X))\to 0$ to the left? 
Apr 22 
comment 
Are Bökstedt's THH manuscripts available?
I could email them to you. 
Apr 16 
answered  Does a fully faithful functor between triangulated categories induce embedding of their Grothendieck groups? 
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 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 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 
comment 
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 4 
answered  What is the applications of the dgenhancements 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_ngeometry 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 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 
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 