Newest Questions
166,651 questions
2
votes
0
answers
36
views
What are the terms in the Eagon Northcott complex?
Let $E \to F$ be a map of vector bundles on a scheme $X$ of ranks $e, f$ (actually, I hope $X$ may be a stack here). Suppose $e \leq f$. I want to describe the locus $D \subseteq X$ where $E \to F$ ...
- 1,154
4
votes
0
answers
37
views
Examples of cocomplete categories without equalizers
What are some examples of cocomplete categories without equalizers? And what are some examples of cocomplete categories without binary products?
They must exist, but at the moment I don't know any. Of ...
- 66.2k
0
votes
0
answers
30
views
Interpretations of the tangent Chern numbers of the complex projective spaces $CP^n$?
I've identified the generating functions for the tangent Chern numbers of the complex projective spaces $CP^n$ given in "Algebraic topology of the Lagrange inversion" by Victor Buchstaber ...
- 11.2k
1
vote
0
answers
56
views
Does a continuous variation through compact $n$ dim manifolds preserve topology?
I begin by writing the definition below that tries to capture what a continuous family /path of manifolds is. The underlying motivation behind the definition is that the transition maps should be ...
- 1,441
2
votes
0
answers
52
views
Triangulated manifolds with local orientation reversal
For a (smoothly) triangulated $n$ manifold $M$, I'll say that the triangulation is amphichiral if it admits an orientation-reversing automorphism. I'll say that the triangulation is locally ...
- 239
0
votes
0
answers
37
views
Explosion of the moment of double stochastic exponential
We consider the stochastic system
$$\frac{dS_t}{S_t}=-R_t\,dW_t,$$
with
$$dR_t=-R_t\,dt-R_t\,dW_t, \quad R_0>0.$$
We conjecture, and would like to show that
$$\mathbb{E}[S_t^2]
=
S_0^2\,\mathbb{E}\...
- 696
14
votes
2
answers
836
views
Was Fermat's Last Theorem known for infinitely many primes before Wiles?
Before Andrew Wiles's 1997 proof of Fermat's Last Theorem, in 1985, Étienne Fouvry et al. proved that the first case of FLT holds for infinitely many primes $p$.
Is there any infinite class of primes ...
- 1,125
0
votes
0
answers
84
views
System of divergence free vector fields
Let $\Omega \subset \mathbb R^p$ be a convex, bounded domain with a smooth boundary. Let $a_{ij} : \Omega \to \mathbb R_+$ be a non-negative smooth function for $i, j \in \{1, 2\}.$ I am interested in ...
- 105
0
votes
0
answers
22
views
Let G be a finite group such that for every natural n the number of solutions to x^n=e is smaller/equal to n. Prove G is cyclic [migrated]
I received this question as homework for a graduate-level course. I don't want the full answer, just a hint on how to proceed with my current direction.
I reduced the problem to the following case: ...
- 11
1
vote
0
answers
38
views
Number of connected acyclic gentle tree algebras
Let $X_n$ denote the number of acyclic connected gentle tree algebras (given by quiver and admissible relations over a field) with $n$ simple modules. Those are also exactly the connected quiver ...
- 28.5k
2
votes
1
answer
176
views
Identity using $\varphi(n), d(n)$ and $\sigma(n)$
Let
$\varphi(n)$ be the Euler totient function.
$d(n)$ be the number of divisors of $n$.
$\sigma(n)$ be the sum of the divisors of $n$.
$a(n)$ be A344598, i.e., an integer sequence such that $$ a(n) =...
5
votes
0
answers
82
views
Constructive status of the meta-theory of intuitionistic propositional logic
Intuitionistic propositional logic has several kinds of models. Bezhanishvili and Holliday [1] showed that these models form a neat hierarchy:
Kripke
Beth
Topological
Dragalin
Heyting
in the order ...
- 150
0
votes
0
answers
25
views
A problem about the vector-valued error estimate for multivariate Hermite interpolation
I am reading an Hermite interpolation method on manifold which is in Section4 in HERE, the core idea is as follows.
Set $dim(\mathcal{M})=m$. We construct an interpolation $\hat{f}_{\tan }: \mathbb{R}^...
- 1,051
-2
votes
0
answers
78
views
Why do continuous analytic tools fail against discrete arithmetic congruences? [closed]
I am investigating the $p$-adic analytic continuation of the discrete sum $\sum_{i=1}^n i^d \lfloor i^{p^k}/p^k \rfloor$. By writing the sum as $\sum_{m = 0}^n a_m\binom{n}{m}$, we obtain its explicit ...
- 579
-6
votes
0
answers
99
views
Is this proof that $A^3+B^3=C^n$ has no primitive solutions correct? [closed]
I am an independent researcher. This arose in the context of studying the Beal conjecture.
Setup: Factor $A^3+B^3=(A+B)(A^2-AB+B^2)=C^n$. For coprime $A,B$: $\gcd(A+B, A^2-AB+B^2)$ divides $3$. This ...
