bio | website | preschema.com |
---|---|---|
location | Essen, Germany | |
age | 23 | |
visits | member for | 5 years, 3 months |
seen | 2 hours ago | |
stats | profile views | 1,349 |
Jan 23 |
comment |
Connection between quasifibrations and homotopy cartesian squares
Are you looking for something like this fibre-wise characterization: ncatlab.org/nlab/show/…? |
Jan 21 |
awarded | Curious |
Jan 20 |
asked | Characterization of closed immersions at the level of perfect complexes |
Jan 17 |
comment |
Motivation for cyclic (co)homology
One motivation for cyclic homology and its variants is the utility in computing algebraic K-theory. See for example the Goodwillie theorem, [T. Goodwillie, Relative algebraic K-theory and cyclic homology, Ann. Math. 124 (1986), 347–402]. |
Jan 16 |
comment |
Homological algebra is linearized homotopical algebra?
Homological algebra is the homotopy theory of chain complexes. The homotopy theory of chain complexes is equivalent to the homotopy theory of modules over the Eilenberg-Mac Lane spectrum $H\mathbf{Z}$. Hence homological algebra is a stable, linear version of the homotopy theory of spaces. See [Stefan Schwede, Brooke Shipley, Stable model categories are categories of modules, Topology 42 (2003), 103-153]. |
Jan 16 |
comment |
Relationship between Hochschild cohomology and Drinfeld centers
@SamuelM, according to Remark 1.5 in the paper, it seems that the Drinfeld centre of $D(A \otimes A^{op})$ will be the $\infty$-category of modules over the Hochschild chain complex of $A \otimes A^{op}$. |
Jan 14 |
comment |
Relationship between Hochschild cohomology and Drinfeld centers
@SamuelM, I think I finally understood what you were really asking. I updated my answer again, let me know if that helps. |
Jan 14 |
revised |
Relationship between Hochschild cohomology and Drinfeld centers
deleted 5 characters in body |
Jan 13 |
comment |
Relationship between Hochschild cohomology and Drinfeld centers
@SamuelM, sorry, I wasn't very clear. I hope the updated answer is more helpful. |
Jan 13 |
revised |
Relationship between Hochschild cohomology and Drinfeld centers
added 1689 characters in body |
Jan 12 |
revised |
Relationship between Hochschild cohomology and Drinfeld centers
deleted 158 characters in body |
Jan 12 |
answered | Relationship between Hochschild cohomology and Drinfeld centers |
Jan 12 |
comment |
Which properties of a variety are detected by its derived category of coherent sheaves?
@მამუკაჯიბლაძე, when taking into account the derived tensor product, one can recover the variety completely (this is a theorem of Thomason and Balmer). |
Jan 12 |
comment |
Which properties of a variety are detected by its derived category of coherent sheaves?
As far as I know, it is not possible to recover the derived category of quasi-coherent complexes from the bounded derived category of coherent sheaves, at the triangulated level. At the level of infinity- or dg-categories, one can recover it as the ind-objects (in the regular case). |
Jan 12 |
comment |
Which properties of a variety are detected by its derived category of coherent sheaves?
The derived category detects homological invariants like (higher) algebraic K-theory, Hochschild homology, cyclic homology, etc. As for cohomological invariants, it is a theorem of Orlov that these are detected up to Tate twists in general, and in some special cases detected completely. |
Dec 18 |
awarded | Popular Question |
Dec 11 |
awarded | Yearling |
Nov 27 |
comment |
Site dependance of the Cech weak equivalences on simplicial sheaves
Just to be clear: you are asking if the weak equivalences in the model structure(s) described at ncatlab.org/nlab/show/… can be described independently of the site of definition, right? |
Nov 17 |
revised |
Use of derivators to the theory of motives?
more appropriate tags |
Nov 17 |
suggested | approved edit on Use of derivators to the theory of motives? |