thel
  • Member for 12 years, 3 months
  • Last seen more than 3 years ago
DG categories in algebraic geometry - guide to the literature?
13 votes

Besides Gaitsgory-Rozenblyum (http://www.math.harvard.edu/~gaitsgde/GL/), you might try looking at Lee Cohn's work (http://arxiv.org/abs/1308.2587), which establishes some equivalence between the ...

View answer
Tensor product of abelian categories
Accepted answer
11 votes

Deligne's article, 'Categories Tannakiennes,' section 5 would be a good place to look. It was published in the Grothendieck Festschrift, vol. 2.

View answer
Is the category of affine schemes (over a fixed field) Cartesian closed?
Accepted answer
9 votes

The existence of such an adjunction implies that $B \otimes -$ preserves limits, which doesn't seem very likely. Here is a counterexample, though probably not the simplest one. Set $B = k[y]$ and ...

View answer
Surveys of Goodwillie Calculus
8 votes

You can get a pretty good birds-eye view by reading this 2004 Oberwolfach report (no. 17): http://www.mfo.de/document/0414/OWR_2004_17.pdf Calculus of Functors is the theme of the 2012 Talbot ...

View answer
Is the Fourier transform of $\exp(-\|x\|)$ non-negative?
Accepted answer
8 votes

This Fourier transform is positive, supported everywhere, and has polynomial decay. It is the Poisson kernel evaluated at time 1, up to some rescaling. http://en.wikipedia.org/wiki/Poisson_kernel

View answer
Topological homotopy category as derived category
7 votes

I don't think this is actually an injection on isomorphism classes. We can see this by restricting to extremely nice spaces, say finite simply-connected CW complexes with free homology. In this ...

View answer
Domains of holomorphy in the complex plane
Accepted answer
7 votes

Let $\zeta_k$ be a countable dense sequence of points in the boundary and consider $f(z) = \sum \frac{1}{2^k} \frac{1}{z-\zeta_k}$. The sum is plainly uniformly convergent on any subset of finite ...

View answer
Whitehead for maps
7 votes

For finite spectra, your question is precisely Freyd's generating hypothesis, which is open.

View answer
Does the truth of any statement of real matrix algebra stabilize in sufficiently high dimensions?
6 votes

Fix an integer $n$. The dimension of a vector space $V$ is divisible by $n$ iff $V$ can be given the structure of a representation of the discrete Heisenberg group $H_n$ with central charge $1$. This ...

View answer
Fixed points sets of pushouts
5 votes

No. Consider the case where your sets happen to be abelian groups with an action of G. Pushing out the zero morphism over any map gives the cokernel, so a special case of your question is whether ...

View answer
sheaves and cosheaves
3 votes

Look at Bredon's 'Sheaf Theory', Chapter Six: "Cosheaves and Cech Homology" I am not aware of any quasi-coherent story.

View answer
How to "fill in" 3-dimensional Laplacian kernels
3 votes

You could just use the 3x3x3 kernel from last time and ignore the extra data, that would be fine, but very wasteful. The payoff for using a big kernel should be a high degree of approximation. You may ...

View answer
Homological algebra for commutative monoids?
3 votes

I can't give a substantive answer to this question, but differential graded abelian monoids have been sighted in the wild here: A Chain Functor For Bordism Author(s): Stanley O. Kochman Source: ...

View answer