Recently Active Questions
159,052 questions
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Examples of finite local rings of length 2 or 3
What is an example of a finite local rings, that has length 2 or 3?
I want something different from $F_{q}[x] / x^{i}$ for $i=2, 3$; I'm looking for something more interesting. If you can give me ...
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Smooth structures on PL 4-manifolds
Is it known whether $O(4) \to PL(4)$, the map from the orthogonal group to the group of piecewise linear homeomorphisms of $\mathbb{R}^4$, is a homotopy equivalence? By smoothing theory for PL ...
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Actions of finite permutation groups on hereditarily finite sets.
Model theorists have a lot to say about so-called definable imaginary elements of a structure. One way to formulate imaginaries is the following: Suppose $\mathcal{M}$ is a structure with universe $M$,...
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Calculating the "Most Helpful" review
How would you calculate the order of a list of reviews sorted by "Most Helpful" to "Least Helpful"?
Here's an example inspired by product reviews on Amazon:
Say a product has 8 total reviews and ...
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Joins of simplicial sets
Why doesn't the join operation on the category of simplicial sets commute up to unique isomorphism? I mean, aren't products and coproducts commutative up to isomorphism? That leads me to conclude at ...
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A hypersurface with many points
Ok, it's time for me to ask my first question on MO.
Consider the affine curve $Y+Y^q=X^{q+1}$ over the finite field $\mathbf{F}_q$. It's interesting because it has the largest number of points over ...
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Factorization of elements vs. of ideals, and is being a UFD equivalent to any property which can be stated entirely without reference to ring elements?
Why exactly is the unique factorization of elements into irreducibles a natural thing to look for? Of course, it's true in $\mathbb{Z}$ and we'd like to see where else it is true; also, regardless of ...
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Cyclic spaces and S^1-equivariant homotopy theory
I'm trying to understand the relationship between cyclic spaces and S1-equivariant homotopy theory. More precisely, I only care about S1-spaces up to equivalence of fixed point spaces for the finite ...
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Connectivity after Geometric Realization?
Suppose that I have a map of simplicial spaces,
$ f: X_* \to Y_*$,
and that I know that the map on zero spaces $f_0: X_0 \to Y_0$ is n-connected. Can I conclude anything about the connectivity of ...
- 18.2k
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Universal property for collection of epimorphisms
Question Is there a nice universal property which captures the notion of "collection of all epimorphisms out of a given object". Of course I will have to consider two epimorphisms $X \rightarrow Y$ ...
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Decomposition of Hölder continuous functions
Let $\alpha\in(0,1)$ and $\eta\in\Lambda_0^\alpha(\mathbb{R})$ be a compactly supported Hölder continuous function of order $\alpha$. I would like to show that, for any $n\in\mathbb{N}$, it is ...
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How to see meromorphicity of a function locally?
Given a germ of an analytic function on a (compact, for simplicity) Riemann surface, how can one see (locally) whether this is a "germ of meromorphic function"? I.e. if I do analytic continuation ...
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Parity, Balls and Boxes
Start with a distribution $\mu$ on [n], and drop m balls into these n+1 slots independently and according to the distribution &mu. That is, we have iid random variables x 1 through x m ...
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How many embeddings are there of super-Virasoro into n Fermions?
What is the space of N=1 super-Virasoro vertex superalgebras inside the c=n/2 free fermion vertex superalgebra? [Said differently, how many Neveu-Schwartz vectors are there in n fermions?] Answers ...
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N_3 and N_4 periodic and pseudo Anosov auto-homeomorphisms
It is well know that the genus three non orientable surface, N3, has only periodic and reducible auto-homeomorphisms, meanwhile the surface N4 is the first non orientable surface with pseudo Anosov ...
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Which computer algebra system should I be using to solve large systems of sparse linear equations over a number field?
This is related to Noah's recent question about solving quadratics in a number field, but about an even earlier and easier step.
Suppose I have a huge system of linear equations, say ~10^6 equations ...
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Lax Functors and Equivalence of Bicategories?
Lax functors of bicategories were introduced at the very inception of bicategories, and I'm trying to get a better feel for them. They are the same as ordinary 2-functors, but you only require the ...
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Hypercohomology of a dg-algebra
Can someone give me a reference (note I am looking for a reference and not a proof) for the following:
If a complex $C$ has a dg-algebra structure, then the hypercohomology
$H^0R\pi_*C$ has an ...
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Indexing the line bundles over a Grassmannian.
As is well known, the line bundles over *CP*$^1$ are indexed by the integers. My question is how are the line bundles over *CP*$^n$, $n > 1$, and *Gr*$(n,k)$ indexed? Moreover, do there exist any ...
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Tropicalizing the learning
Could someone tell me if it is possible to do tropical geometry with NO knowledge(or with very few) of algebraic geometry (a la Hartshorne)?
By "do tropical geometry" I mean, to understand the ...
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When can one localize Ext?
Let $R\to S$ be a ring map such that $S$ is projective over $R$ (I am willing to assume $S=R[X_1,...,X_n]$). Let $M,N$ be finite $S$-modules. Let $P\in Spec R$ such that $M_P$ is $R_P$-flat. Under ...
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The Discrete Logarithm problem [closed]
I am puzzled with the following discrete logarithm problem:
Given positive integers b, c, m where (b < m) is True it is to ...
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Choice of adviser
Not sure how to tag this one so feel free to edit and add tags.
When I initially started graduate school my choice for an area of study was quite nebulous. I had only figured out enough to know that ...
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Is (relatively) algebraically closed stable under finite field extensions?
Let $F\subset F'$ be a field extension such that $F$ is algebraically closed inside $F'$, i.e. if $x\in F'$ is algebraic over $F$ then $x$ belongs to $F$ itself.
Let now $F\subset L$ be a finite field ...
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How should I think about correspondences?
I know at least two definitions of correspondence, and my question might as well be about both of them.
Let $X,Y$ be objects in your favorite category. A correspondence is a span, namely a diagram $...
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Is there a theory of differential equations for smooth correspondences?
This question is very closely related to another one I just asked. The general question is to what extent there is a theory of differential equations for smooth correspondences (between a smooth ...
CommunityBot
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Are any finitely generated reflexive module a 2nd syzygy?
Are any finitely generated reflexive module a second syzygy?
(I´m thinking especially in normal noetherian domains)
More general...
Are any divisorial lattice a second syzygy?
(I´m thinking ...
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Intuition about schemes over a fixed scheme
I am taking a first course on Algebraic Geometry, and I am a little confused at the intuition behind looking at schemes over a fixed scheme. Categorically, I have all the motivation in the world for ...
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When is a commutative ring the limit of its local rings?
Let $A$ be a commutative ring. Then we get local rings $A_p$ by localizing at each prime ideal $p$. Moreover, we get $A_p \rightarrow A_q$ when $p$ contains $q$. So we get a big diagram indexed by the ...
CommunityBot
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Springer corresponding for nullcones other than the standard nilpotent cone
I understand the ordinary Springer correspondence gives a bijection between orbits in the nilpotent cone for the adjoint representation and irreducible representations of the Weyl group, through ...
- 3,131
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Is there a tool for finding probability distributions given some samples?
I'm looking for a tool that does "probability distribution fitting" given a set of data points. Sort of like curve fitting, but tries to fit to standard density distributions.
For example if I input
...
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Tropical mathematics and enriched category theory
Is there a connection between tropical mathematics and the Lawvere enriched category theory approach to metric spaces? I guess I will give a partial answer to this below, but I mean can they be ...
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Paritioning a set of numbers A into two sets B,C so that abs(prod(B) - prod(C)) is minimal
Let A = $\{a_1,...,a_n\}$ be a set of numbers. We can assume all elements of A are integers.
Is there any efficient way to partition A into two sets B = $\{b_1,...,b_k\}$ and C = $\{c_1,...,c_l\}$ ...
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Can different modules have the same symmetric algebra? (answered: no)
Algebraic geometry allows one to think of an $A$-module $M$ geometrically as a module of functions on the $A$-scheme $\mathrm{Spec}(\mathrm{Sym}(M))$.
I'm wondering if anything is lost in just ...
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A website linking to most major math journals? [closed]
What's your usual action online in order to browse math journals? Like check Arxiv or MathSciNet. Any other good link directs you to most updated articles in major math journals. Or the traditional ...
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complex cobordism from formal group laws?
Reading Ravenel's "green book", I wonder about his question on p.15 "that the spectrum MU may be constructed somehow using formal group law theory without using complex manifolds or vector bundles. ...
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What is a monoidal metric space?
At time of writing, the highest rated answer to my question What is a metric space? is Tom Leinster's account of Lawvere's description of a metric space as an enriched category. This prompted my ...
CommunityBot
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Stable w-length
Let $F$ be a free group, and $w$ an element of $F$. In any group $G$, a $w$-word is the image of $w$ or $w^{-1}$ under a homomorphism from $F$ to $G$. The subgroup of $G$ generated by $w$-words is ...
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Minkowski sum of small connected sets
Suppose that the convex hull of the Minkowski sum of several compact connected sets in $\mathbb R^d$ contains the unit ball centered at the origin and the diameter of each set is less than $\delta$. ...
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Difference Equations & Possible Limits
The answer to this may well be in some elementary textbook - a reference might be more useful than a short answer here.
If we look at the behaviour of a point in R n under matrix multiplication, we ...
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Algebraic Varieties which are also Manifolds
Any non-singular projective variety over $\mathbb{C}$ is easily seen to be a smooth manifold. Presumably the same is not true for algebraic varieties - one would not expect varieties with singular ...
CommunityBot
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A graph connectivity problem (restated)
Given an undirected connected graph, our goal is to remove some edges to make the graph disconnected. The constraint is that each node of the graph can not lose more than $m$ edges incident to it. I ...
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morphisms from abelian varieties to rational curves.
Let $A$ be an abelian variety and and $\sigma$ an automorphism of $A$. Suppose $f:A\rightarrow P^1$ is a morphism. Is it true that $\sigma$ descends to an automorphism of $P^1$? I seem to remember ...
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de Rham Cohomology of surfaces
Does anyone know a good book where I can find the computation of the de Rham Cohomology of surfaces in R^3 and other classical manifolds (higher dimensional spheres and projective spaces for example) ?...
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When is an Albanese variety principally polarized?
Let (X,x) be a pointed projective variety. Then there exists an abelian variety V which is universal for maps of pointed varieties $(X,x) \to (A,e_A)$, called the albanese variety. When X is a curve, ...
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What cohomology theories would be interesting for nilpotent cones/nullcones?
As I understand, when we have a nilpotent cone, or a nullcone of a Lie group representation, what seems to be done in a lot of the literature (e.g. Achar&Henderson-"Orbit closures in the enhanced ...
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Topological Langlands?
In a workshop about the geometry of $\mathbb{F}_1$ I attended recently, it came up a question related to a mysterious but "not-so-secret-anymore" seminar about... an hypothetical Topological Langlands ...
CommunityBot
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Algorithms for semistable reduction of families of curves
This is a somewhat vague question which came up MSRI a few days ago: Suppose I have a family of curves over a one dimensional base, given in a computationally explicit way. For example, maybe I have a ...
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On algebraic tubular neighbourhoods and Weak Lefschetz
Can one formulate those version of Weak Lefschetz that uses tubular neighbourhoods purely in terms of cohomology of (some) algebraic varieties?
Theorem in 5.1 of Part II in Goresky-MacPherson's "...
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Complexes of representations with complementary central charges
This is another question asking for references. There is an important phenomenon of correspondence between (complexes of) representations of infinite-dimensional Lie algebras with the complementary ...
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