8
votes
Theory of $n$-truncated $A_\infty$ categories/functors?
$A_n$-spaces are already discussed in the original paper of Stasheff, Homotopy associativity of H-spaces, I and II.
In the linear setting, $A_n$-algebras are discussed e.g. in A∞-algebras, spectral ...
- 8,385
8
votes
Accepted
Reference request: The non-productivity of Lindenbaum numbers
Karl-Heinz Diener proved in On the transitive hull of a κ‐narrow relation that for all class relations $R$, if $R$ is $\kappa$-narrow in the sense that $\aleph^\ast(R^{-1}[\{x\}])\leqslant\kappa$ for ...
- 1,782
6
votes
Accepted
Grothendieck purity for Brauer groups of stacks
The relevant result is now in the literature.
It first appeared as Proposition 8.1 in On Brauer groups of tame stacks by Anchenjang. Actually he proves the result for all algebraic stacks smooth over ...
- 388
5
votes
Accepted
Reference request for elementary convex geometry property
Indeed, this can be proved more simply, and in greater generality -- assuming only that the support of $P$ is contained in $C$ (rather than in $\mathcal X$).
Indeed, without loss of generality the ...
- 128k
4
votes
Accepted
Vector bundles over a Stein space are projective
I suppose you were given essentially a reference in the comment. Alternatively, to expand a little on the proof of this fact that I mention in the answer above the linked comment, to me this argument ...
- 1,457
4
votes
On a probabilistic integer factorization algorithm given bounds for one prime factor
If $D\le 3$, it is known how to do this in polynomial time by Coppersmith's algorithm [Cop96]: note that $q \approx N^{\frac{D}{D+1}}$ and therefore $B_2-B_1 \approx q^{\frac{D-1}{D}} \approx N^{\frac{...
- 5,382
3
votes
Comments and reference-request on books for KK-theory
Here is a very rough outline of the proof of the index theorem using KK-theory:
Define $KK_G(A, B)$, where $G$ is a Lie group and $A$ and $B$ are
[adjectives] C*-algebras, and the Kasparov product ...
- 29.2k
3
votes
In search of a $q$-analogue of a Catalan identity
If the identity were to be rewritten as:
\begin{equation}
\sum_{k=0}^n 2 C_k \binom{2(n-k)}{n-k} = \binom{2n + 2}{n+1},
\end{equation}
here is a $q$-analog:
\begin{equation}
\label{eq:q-cbc-cat}
\sum_{...
- 31
3
votes
Laplacian on manifolds and random matrix theory
This is somewhat different since the metrics are not generic, but there is a natural way to define the space of hyperbolic surfaces of a fixed genus. There has been a large amount of research studying ...
- 6,001
2
votes
Vector bundles over a Stein space are projective
Corollary 2.6.5 in Forstnerič "Stein Manifolds and Holomorphic Mappings". (2nd Edition)
- 1,466
1
vote
Coradical filtration for comodules is exhaustive
Exhaustiveness of the coradical filtration of a coalgebra is proven in Theorem 5.2.2 of Montgomery's book "Hopf algebras and their actions on rings." This is not as general as what you asked ...
- 1,335
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