Reputation
3,224
Next privilege 5,000 Rep.
Approve tag wiki edits
Badges
1 20 36
Impact
~57k people reached

Dec
13
comment Derived equivalent varieties with differing integral Mukai-Hodge structures?
@MikhailBondarko, it's not quite so easy, I'm afraid. You would need to be able to define Betti cohomology and Hodge structures at the level of dg-categories, something which is most likely impossible in my opinion. The best you have are noncommutative Hodge structures on Hochschild homology and variants, studied by Kaledin and others.
Dec
13
comment Generalized Euler characteristics of non-motivic origin
@MikhailBondarko, that's right, it was also proved directly in the note of Orlov (the proof essentially amounts to the same thing as the comparison of noncommutative motives modulo Tate twists with usual motives, namely Grothendieck-Riemann-Roch).
Dec
11
awarded  Yearling
Dec
10
awarded  Nice Question
Dec
10
comment Derived equivalent varieties with differing integral Mukai-Hodge structures?
This is related to my question: mathoverflow.net/questions/152345/…
Dec
10
comment Generalized Euler characteristics of non-motivic origin
It's actually a conjecture of Orlov, see this paper. (The conjecture is for rational coefficients as it is clearly false integrally. I agree that it is not really expected to be true even rationally, though.)
Dec
10
comment teaching higher algebra
In 2013 in Berlin, Timo Schürg gave a course on a low-tech (model categorical) introduction to the deformation theory of simplicial commutative rings. The notes are available here. It was attended by algebraic geometry students mostly, and was pretty successful I think.
Dec
9
comment reference request for mod p and p-adic K-theory
See also these notes of Mitchell which are an exposition of Quillen's proof.
Dec
1
comment Is Carlos Simpson's Descent available online?
Here is a link: dropbox.com/s/j0ft4tiop740wjv/SIMPSON%20Descent.pdf?dl=0 (I don't remember where I found this.)
Nov
26
comment K theory long exact sequence
@DmitryVaintrob, statements to this effect are in Blumberg-Gepner-Tabuada. They show that K-theory preserves filtered colimits and split exact sequences.
Nov
25
answered K theory long exact sequence
Nov
23
comment Categorical or simplicial introduction to modern homotopy theory
For Blakers-Massey at least, there is a nice model independent proof described in a note of Rezk.
Nov
13
awarded  Custodian
Nov
13
reviewed Approve Irrationality of $ \pi e, \pi^{\pi}$ and $e^{\pi^2}$
Oct
31
comment Algebraic geometry introduction for homotopy theorists/algebraic topologists
At a more basic level, I think that the "functor of points" approach to algebraic geometry is much clearer to students comfortable with homotopy theory or category theory. So one might prefer to read something like Toen's course notes, before reading a scheme theory book.
Oct
30
awarded  Enlightened
Oct
30
awarded  Nice Answer
Oct
28
revised Geometric morphism of $\infty$ topos
deleted 1 character in body
Oct
28
answered Geometric morphism of $\infty$ topos
Oct
15
comment A tensor product for triangulated categories?
There is some discussion of this question in an old paper of Bondal-Larsen-Lunts (arXiv:math/0401009).