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159,068 questions
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How would you compute that "average" ?
I created a DJ-ing application that allows you to mix your MP3s with a real turntable.
So I generated an audio timecode to burn on a CD, left channel is the absolute position, right channel is a ...
CommunityBot
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2
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orthogonality relation for quadratic Dirichlet characters
Hello,
I've been working deriving the orthogonality relation for quadratic Dirichlet characters $\chi_d(n)$ (or real primitive characters). The statement I'm trying to prove is
$$\lim_{X \...
- 4,671
4
votes
2
answers
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Degree of divisors and degrees of the corresponding maps to projective space
Suppose I have a divisor $D$ on a curve $X$ (Hartshorne curve - smooth, projective, dimension one over an algebraically closed $k$). If the complete linear system $|D|$ is basepoint free then I get a ...
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3
answers
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Is every flat unramified cover of quasi-projective curves profinite?
When I first learned about the etale fundamental group, there was a mythical theorem going around that in the algebraic case all we need to look at is the finite covers, because the infinite degree ...
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8
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2
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Constructing the Hecke-Algebra from the Burau representation
I'm currently learning about knot theory, so please correct me if I'm saying something senseless. I'll try to describe the things just as I think they are.
First, suppose we have constructed the ...
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6
votes
1
answer
887
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Linear algebra lemma
The following Lemma is in Beauville-Donagi, and I always took it for granted. Now I've tried to find a proof, but got stuck. They say it is a really simple lemma, so I may just be overlooking ...
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1
vote
3
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391
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Numerical algorithms on mixed-precision computational models.
I want to learn more about numerical algorithms that use mixed-precision computational models (where instead of everything being 32/64 bit floating points, we can do lower precision calculations at ...
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1
answer
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Equality in the union bound.
Lemma: Let $A_1,\ldots,A_n$ are events $n\in\mathbb{N}$ then
$$
\sum_{i=1}^n \mathbb{P}(A_i) = \mathbb{P}(\cup_{i=1}^n A_i)
$$
if and only if $A_1,\ldots,A_n$ are mutually exclusive.
Both ways are ...
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6
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1
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Sparse approximate representation of a collection of vectors
Suppose I have a collection of $n$ vectors $C \subset \mathbb{F}_2^n$. They are of course spanned by the canonical set of $n$ basis vectors.
What I would like to find is a much smaller (~ $\log n$) ...
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V-filtration of D-modules associated to a monomial
Hi
In Mixed Hodge modules Saito computes the Verdier specialisation of a D-modules with respect to a monomial $g = x_1^{m_1}\ldots x_n^{m_n}$. This is a very nice result as I find such explicit ...
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5
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1
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Quillen's Morphism Inverting Functors
In "Higher algebraic K-theory I" Quillen defines a morphism inverting functor to be a functor from a category C to the category Sets which maps "arrows" in C to isomorphisms in Sets.
Proposition 1:
...
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4
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Kähler manifold which is not algebraic
Can someone provide examples of Kähler manifolds which are not algebraic?
This question came to my mind seeing the post of Andrea Ferretti.
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0
answers
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Is my definition of a context algebra new?
In my DPhil thesis, I defined what I called a context algebra as a model of meaning in natural language. The idea is to mathematically formalise the notion that meaning is determined by context. It ...
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2
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Algebraicity of the completion of a field? Finiteness?
At the end of my 8410 class today (see http://alpha.math.uga.edu/~pete/MATH8410.html if you care), one of my students asked me the following very interesting question:
Let $(K,|\ |)$ be a normed field,...
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5
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Killing the torsion in homotopy
Origin
This question was asked by John Baez in This Week's Finds in Mathematical Physics (Week 286). Therefore, please don't upvote this question (unless you really want to), but do upvote the ...
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4
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2
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elliptic curve with j-invariant T
This is the exercise on Serre's book "l-adic abelian representations". on Section I-5.
Notation: Galois group $G$ acts on $T_{\ell}(E)$, the Tate module representation, $G_{\ell}$ is the image of $G$ ...
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1
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A closed subscheme of an open subscheme that is not an open subscheme of a closed subscheme?
A morphism $f: V \rightarrow X$ of schemes is a locally closed immersion if it can be factored into a closed immersion followed by an open immersion. It is not hard to show that if $f$ is an open ...
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6
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Do finite places of a number field also correspond to embeddings?
Something that seems to be pretty standard in every introductory treatment is that the infinite places correspond to embeddings into $\mathbb{C}$. Do the finite places correspond to embeddings as ...
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4
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Are all mathematical theorems necessarily true?
Define a formal tautology as a statement where by the nature of its atomic components there exists no truth-value assignment where it is not true. A contingent statement is a statement that is true by ...
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1
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an exercise on integrality of characteristic polynomials
Suppose A is a matrix with coefficient in $Q_{\ell}$, and all the coefficients of its char. polynomial are in $Z$ (thus an integral polynomial). Prove that the char. polynomial of $A^n$ is also ...
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Reference for Tate vector spaces
... aka locally linear compact vector spaces. The one reference I know is http://www.math.harvard.edu/~gaitsgde/grad_2009/SeminarNotes/Nov3-10(CentExt).pdf. Does anyone know another good reference?
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What does primary mean geometrically?
Given a primary ideal I in a ring A, we can consider the subscheme V(I) of Spec(A).
It is a nilpotentification (?) of the integral subscheme V(rad(I)) given by the radical rad(I) of I.
My question is ...
- 57.6k
0
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1
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Divisor Intersections and Chern Class Products
For a real algebraic variety, is the integral of the product of the Chern classes of two line bundles equal to the intersection number of the two corresponding divisors?
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4
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Number theory textbook with an algebraic perspective
Most of the number theory textbooks I've dealt with take a very classical approach to the subject. I'm looking for a textbook that's something like a first course in number theory for people who have ...
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1
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Maximal subgroups of abelian groups and Q-algebras
Let $G$ be an abelian group which does not have a maximal subgroup. Does it follow that $G$ is a $\mathbb{Q}$-algebra?
It is easy to see that $\mathbb{Q}$-algebras do not admit any maximal subgroups. ...
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To what extent does (co)homology of groups made discrete depend on set theory?
There's a well-known paper by Milnor, "On the homology of Lie groups made discrete," that discusses the relation between the homology of a Lie group $G$ and the underlying discrete group $G^\delta$. ...
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Are there analogues of Desargues and Pappus for block designs?
Finite projective planes are fascinating objects from many perspectives. In addition to the geometric view, they can be viewed as combinatorial block designs.
From the geometric perspective, there ...
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10
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Asymptotic non-distortion of the separable Hilbert space
By the work of E. Odell and Th. Schlumprecht, we know that the
separable Hilbert space $\ell_2$ is arbitrarily distortable. But
I don't know if an "asymptotic" version of their result is true.
To ...
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0
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1
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Reference on a result on representation of moderate growth
Let G be a real reductive group, and P any parabolic subgroup. In the paper 'Canonical extensions of Harish-Chandra modules to representations of $G$' by Casselman, a result says that if we begin with ...
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3
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Can infinite first-order categories be specified other than as categories of models?
I am glad to see that a general question like Is there a relationship between model theory and category theory? receives quite a lot attention and no down-votes for being too general and unspecific. ...
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1
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When do two objects become isomorphic in the stable category?
I'm afraight this might be obviously true or false, but anyway: Let $({\mathcal A},{\mathcal E})$ be a Frobenius category and $X,Y\in{\mathcal A}$. If there exist projective-injective $P,Q\in{\mathcal ...
- 47.3k
8
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1
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Can minimal surfaces be characterized by some universal property?
As objects which are minimal (in some respect), this seems entirely plausible, but I'm not sure what category we should be working in, and what restrictions we would need, to actually have a situation ...
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3
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How many trial picks expectedly sufficient to cover a sample space?
Consider a sequence of independent events where an $r$ element subset of an $n$ element set is picked uniformly randomly (ie. any of the $\begin{pmatrix}n\newline r\end{pmatrix}$ possibilities being ...
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Solving a noisy set of linear equations.
Suppose we have a square $n\times n$ real matrix $A$ of full rank such that the squares of the elements in each row sum to 1, an $n\times 1$ vector of variables $x$, and an $n\times 1$ real vector $a$,...
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Are Fukaya categories Calabi-Yau categories?
Let X be a compact symplectic manifold. There is an idea, I think probably originally due to Kontsevich, that we should be able to get Gromov-Witten invariants of X out of the Fukaya category of X. ...
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2
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addition of definable numbers decidable?
Define a number generating machine to be a total turing machine running on input alphabet {0,1} (or, any ary), that given input n (in binary) outputs a digit (binary or decimal or whatever).
Given ...
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15
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1
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Frobenius Descent
Let $S$ be a scheme of positive characteristic $p$ and $X$ a smooth $S$-scheme. Let $F:X\rightarrow X^{(p)}$ denote the relative Frobenius. A result by Cartier (often called Cartier descent or ...
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2
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3
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variance of $1/(X+1)$ where $X$ is Poisson-distributed with parameter $\lambda$
What is the variance of $1/(X+1)$ where $X$ is Poisson-distributed with parameter $\lambda$! The series for the second moment is horrible!
$E({1\over (X+1)^2})=\sum_{k=1}^{\infty}\frac{1}{k^{2}}\frac{...
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2
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657
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Properties of the class of topological spaces possessing a CW-structure
Let ${\mathcal C}$ be the class of topological spaces which carry a CW-structure (note that I do not want to fix some particular CW-structure).
Is it true that for a covering map $E\stackrel{f}{\to} ...
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Stokes' theorem etc., for non-Hausdorff manifolds
This question is prompted by another one.
I want to motivate the definition of a scheme for people who know about manifolds(smooth, or complex analytic). So I define a manifold in the following way.
...
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21
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5
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Nonsingular/Normal Schemes
I always had trouble remembering this. Is it true that a curve over a non-algebraically-closed field is normal implies that it's non-singular? How about a 1 dimensional scheme? How about dimension 2? ...
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4
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Can isomorphisms of schemes be constructed on formal neighborhoods?
Let (A,m) be a complete local Noetherian ring and let X and Y be two schemes of finite type over A (and flat over A). Let Xn and Yn be the reductions of X and Y mod mn+1.
Question: Suppose there is ...
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1
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Lower bound for Jacobian of matrix exponential map near origin
What is a lower bound for the Jacobian of the exponential map from the skew-symmetric matrices to the orthogonal matrices near the origin?
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What is the standard reference on "infinitesimal space" in algebraic geometry??
infinitesimal 'spaces' is a serious issue in noncommutative (and commutative) geometry: they serve as a base of a Grothendieck-Berthelot crystalline theory and are of big importance
for the D-module ...
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Weil Conjectures for nonprojective algebraic varieties
If we replace projective variety with algebraic variety in the statement of the Weil conjectures what happens? To me it seems the statement still makes sense. But is it still true?
- 65.4k
3
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A strange logical implication in algebraic geometry
So there's an old theorem of Lang and Weil showing that the Riemann hypothesis for curves over finite fields implies a kind of quasi-riemann hypothesis for surfaces over finite fields.
I am wondering:...
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3
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2
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tamely branched cover over P^1
k is an algebraically closed field, X is a smooth, connected, projective curve over k. f: X-->P^1 is a finite morphism. Let t be a parameter of P^1, suppose f is etale outside t=0 and t=\infty, and ...
- 65.4k
16
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Coarse moduli spaces over Z and F_p
I would like to know to what extent it is possible to compare fibers over $\mathbb{F}_p$ of coarse moduli spaces over $\mathbb{Z}$, and coarse moduli spaces over $\mathbb{F}_p$. I ask a more precise ...
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Class groups of normal domains over finite fields
Let R be a local, normal domain of dimension 2. Suppose that R contains a finite field. I am interested in knowing when the class group of R is torsion. In characteristic 0, this is known to be ...
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4
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2
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What does univoque mean?
This seems to be a french word that is used in English language mathematical papers. It seems to mean something like "unambiguous." What is its technical definition?
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