Recently Active Questions
159,041 questions
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Shifted Dirichlet series
If $\sum_{n=1}^\infty \frac{a_n}{n^s} $ converges, does
$\sum_{n=1}^\infty \frac{a_n}{(n+1)^s} $ also converge?
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What is $\overline{\text{Spec}\mathbb{Z}}$?
In Connes work on the Riemann Hypothesis he talks about constructing $\overline{\text{Spec}\mathbb{Z}}$ as a curve over the field with one element. I just want to know what Spec means. Is the same as ...
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increasing bijection
Using the back-and-forth method we can construct an increasing bijection from the set of rational numbers to the set of of rational numbers except zero.
http://en.wikipedia.org/wiki/Back-and-...
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Simplicial set notation and vocabulary question.
Notation question:
What does $(\Delta^1)^{ \{1, \ldots,n-1 \}}$ denote? UPDATE: I (David Speyer) tried to fix the LaTeX. Please see if I got it right.
Vocabulary question:
Suppose $z:\Delta^{n+1} \...
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Simple applications of Atiyah-Bott localization
I am looking for some simple and concrete -- but still non-trivial and illustrative -- applications of Atiyah-Bott localization in the context of equivariant cohomology.
Do you know any good ones?
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Total Spaces of Quasicoherent Sheaves
You can construct a total space of a quasicoherent sheaf on an scheme by taking relative spec of the symmetric algebra of the dual sheaf. For locally free sheaves, you get vector bundles, and every ...
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2
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algebraic equivalence of divisors
for the embedding defined by very ample divisors, if they are lin. eq, then the embeddings are the "same" (up to a linear transformation). What do we know if given that the divisors are algebraically ...
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Coxeter Arrangements and an Identity
Let $\{A_i\}$ be a collection of $m$ hyperplanes in $\mathbb{C}^n$ which all pass through the origin (a central hyperplane arrangement). Such an arrangement is called Coxeter if reflecting across any ...
- 156k
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Does there exist a meromorphic function all of whose Taylor coefficients are prime?
More precisely, does there exist an unbounded sequence $a_0, a_1, ... \in \mathbb{N}$ of primes such that the function
$\displaystyle O(z) = \sum_{n \ge 0} a_n z^n$
is meromorphic on $\mathbb{C}$?
...
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The 2-sphere and $\mathbb{CP}^1$
As is very well known, the algebraic variety $S^2$ is isomorphic to projective variety $\mathbb{CP}^1$ as a complex manifold. As is also well known, the coordinate ring of $S^2$ is given by $< x,y,...
- 56.6k
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Which fortuneteller is better
We have a probability game, where we have $N$ number of events, each of which outcome can be $A,B$ or $C$. We do/will NOT know real probabilities afterwards: only the discrete outcome ($A, B$ or $C$) ...
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Does the equation x^10+y^10+z^10=t^2 have positive integer solutions? [closed]
Does the equation x^10+y^10+z^10=t^2 have positive integer solutions? What's the best approach to determine this? What's possible method to prove if 95% that there are no solutions?
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Splitting book into chapters [closed]
I need a way to split output pdf-file (a book) into chapters on such a way that cross-references will survive.
A simple example with a solution (based on answers below) can be found here
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Can an infinite conjugacy class in a group split into more than one conjugacy class in some subgroup of finite index?
Are there some theorems about the splitting of infinite conjugacy classes into several conjugacy classes in a subgroup? I am mainly interested in subgroups of finite index. Thanks.
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Why is algebraic geometry so over-represented on this site? [closed]
Seriously. As an undergrad my thesis was on elliptic curves and modular forms, and I've done applied industrial research that invoked toric varieties, so it's not like I'm a partisan here. But this ...
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When is a Hausdorff space metrisable?
This question may be a little too easy for this site, but I'll ask it anyway: when is a Hausdorff topological space metrisable?
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Is the total space of a module connected?
Let $A$ be a ring and $E$ a module. If $\mathrm{spec} A$ is connected, then so is $\mathrm{spec} S^\bullet E$. If this is not true in general, then what are some minimal conditions that make it true?
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"Right" Way of Introducing Modular Forms to Undergraduate Audience?
I am giving an extremely short talk (~12 minutes) in a few weeks in which I need to be able to introduce and motivate the idea of a classical modular form to an audience of undergraduates in as short ...
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Expectation of the product of almost independent Gaussians
Let $X_ i$ be copies of the standard real Gaussian random variable $X$. Let $b$ be the expectation of $\log |X|$. Assume that the correlations $EX_ iX_ j$ are bounded by $\delta_ {|i-j|}$ in absolute ...
- 61.9k
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Cohomology of associative algebras
Let $A$ be an associative algebra over a commutative ring $k$. I've read statements saying that Hochschild (co)homology is the "right" notion of (co)homology for associative algebras. When $A$ is ...
- 1,680
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Extending kaehler property to desingularizations of quotients
Be $T$ a complex torus (which is not necessarily am abelian variety) of complex dimension $n \geq 2$. On $T$ we have an involution corresponding to the $(-1)$ application (i.e. passing to the inverse ...
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Real and Complex Projections
A projection $P$ on a real vector space is defined to be a linear mapping such that $P^2 = P$. For projections on complex vector spaces why does one require the extra condition that $P^* = P$, where $...
- 5,992
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Properties of adjacent submatrixes [closed]
Hi!
I've encountered a matrix problem when designing an algorithm, which I cannot seem to figure out. I have a (square) matrix with the following properties:
j<k → aij<aik, aji<aki
aij&...
- 5,992
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Algebraic Statistics textbook
Hey
A friend and I are thinking of having an algebraic statistics seminar next semester. Does anyone know of a good book to try learn it out of?
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correspondence between invariant forms and Lie groups
In Lie theory, one often asks about alternating forms on $\mathbb{R}^n$ which are invariant under some particular subgroup $G\subseteq GL_n(\mathbb{R})$, and there is always some algebra of invariant ...
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Transformations induced by geodesics of boundary
I have a general question in Riemannian geometry:
Let M be a compact manifold and $\partial M \neq \emptyset$. Then shoot a geodesic from any boundary point perpendicularly into the interior of M. How ...
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Upper bound on the area of a midpoint pentagon?
Starting with a convex pentagon P, we define the "middle polygon" Q, whose vertices are the middle points of the sides of the initial pentagon. The ratio between the areas of this polygons seem to ...
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4
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Deconvolution of gamma distributions
If the sum of two independent random variables is gamma distributed does this imply that the individual random variables are also gamma distributed. I suspect that the answer is no, but I do not know ...
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How do I describe a fusion category given a subfactor?
I felt like following up on Kate's question. There were some good motivational answers there.
Given a pair of factors M < N, there is a standard way to construct a 2-category whose objects are M ...
CommunityBot
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In an n-dimensional linear 2nd-order ODE, why is the transpose-inverse to a system of solutions also a solution?
I'm at a sticky spot in my research. Namely, I have a particular fact, and it ought to have a short proof, but the only way I know how to show it is long and drawn out, and I don't like it and worry ...
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free homotopy groups -- when do they exist?
Let (X,x) be a pointed space. There is an action of π1(X,x) on πn(X,x) -- determined by considering πn(X,x)=πn-1(ΩxX,x), where ΩxX denotes the space of loops in X based at x, ...
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R2 and S3 for rings.
For a noetherian ring R, Serre's criterion for normality states that R is normal if and only if R satisfies conditions R1 and S2, where R1 is regularity in codimension one, and S2 is Serre's condition ...
- 15.1k
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Factoring maps of handlebodies
Any map of finite graphs (1-dimensional CW-complexes) factors as a composition of
a finite sequence of folds;
an inclusion; and
a finite-to-one covering map.
There should be a corresponding result ...
- 28.2k
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3
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How to sufficiently motivate organization of proofs in math books
Hello,
I have a bit of a general question about math books. I get the feeling that in a lot of math books, the organization for the theorems and lemmas are not explained well (ex. Topics in Algebra ...
- 1,861
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4
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Beamer hints and tips [closed]
I deleted a rant from this question because I felt it detracted from the given answer to the specific question. However, beamer is the "new kid on the block" in terms of giving talks (not that new!) ...
CommunityBot
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Explicitly describing extreme points of infinite dimensional convex sets
I am currently trying to apply some results from Choquet theory - i.e., the generalisation of results by Minkowski and Krein-Milman for representing points in a compact, convex set C by probability ...
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Understanding formula in Frenkel-Witten
I'm not the person to understand everything in Geometric Endoscopy and Mirror Symmetry, but some parts of it are reasonably clear to me.
In particular, one of the main objects, mathematically ...
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3
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How do we know that a map $f: U \to Y$ extends to $\bar{U}$?
I read the following fact: if $U$ is an open subset of $P_k^1$ and $f: U \to U$ is an automorphism of schemes, then $f$ extends to an automorphism of $P_k^1$. Thus I was curious: is there a general ...
- 156k
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"Positive systems" in n * the (n-1)-simplex
Let S := the nonnegative integer solutions to {$a_1 + ... + a_n = n$},
and center := (1,1,1,...,1).
Call a vector v generic if v.s = v.center <=> s = center.
Then each generic v defines a positive ...
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Cohomology map induced by the group actions on homogeneous vector bundles
Here is a topological question which seems quite elementary. The answer to this question may be useful e.g. in estimating the orders of the automorphism groups of some algebraic varieties and in ...
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485
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Estimating probability of set membership
I have a number of discrete finite sets, $A_0$ through $A_n$. I do not actually know their contents, but I know the size of each set and the size of the intersection between $A_0$ and each of the ...
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3
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Dense section of sheaves of modules
Here is something that isn't yet very clear to me. Say, I've got a commutative ring A. I consider the affine scheme from A, so it's a sheaf of rings over Spec A.
EDIT: And additionally let's say ...
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Is there any Grothendieck Riemman Roch theorem for general stack ?
It seems that there is no g.r.r for stack yet according to dejong. Does anyone know anything about it? But as you might know, there are some complex manifold which is not scheme having atiyah singer ...
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Finding correlation in large data, non-numeric sets
Suppose I collect a lot of data from a group of persons, like
their height
their weight
color of eyes (chosen from eg the four categories blue/brown/black/other)
sex
day of the week the measurement ...
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Comparing maps of reduced schemes
Nice fact:
Suppose f:X->Y is a map of schemes and Z⊆Y is a subscheme (locally closed immersion) containing the set-image of X. If X and Z are reduced, then it follows that f factors through Z. ...
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Any work on the Adams-Watters triangle?
Does anyone know whether any arithmetical or asymptotic results have been obtained about the Adams-Watters triangle?
- 15.1k
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What is a formula for the "group-like Drinfeld element"?
Any quantized universal enveloping algebra (in fact, any toplogically quasi-triangular Hopf algebra) has an (in its completion) an element u called the Drinfeld element which gives an isomorphism from ...
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Quantum Frobenius II
In a previous question, I asked how Lusztig's quantum Frobenius generalizes the classical Frobenius map on a variety over a finite field. I was directed to a very interesting paper by Kumar and ...
CommunityBot
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cosimplicial algebras to dg-algebras
The normalized Moore complex functor is usually considered taking simplicial abelian groups to chain complexes. But there is an obvious dual version that takes cosimplicial abelian groups to N-graded ...
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For which integers u,v does au=bv *approximately*? [closed]
Given two positive integers a,b what is the minimal integer n, so that there exist two positive integers ...
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