All Questions
5,076 questions with no upvoted or accepted answers
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Changing basis on an extension of a free Z-module.
Consider a finite-rank free $Z$-module $Y$. Let $c: Y \times Y \rightarrow Z$ be a $Z$-bilinear form. Assume that $c(y_1, y_2) + c(y_2, y_1)$ is even, for all $y_1, y_2 \in $. Then $c$ "incarnates"...
- 13.3k
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313
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Quick references/sources for the hyperbolic Riemann Surfaces with boundary
Hello,
Here I am asking for a reference for the universal cover of hyperbolic Riemann surfaces with geodesic boundaries. For example, I want to know how the universal cover/fundamental domain of ...
- 1,471
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209
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convergence of multiple integral
I am searching for some theorems and books about convergence of multiple integrals of the form:
$$
\int_{-\infty}^{\infty}\int_{-\infty}^{\infty}\;f(x,y)\;\mathrm{d}x\,\mathrm{d}y.
$$
In particular, ...
- 101
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332
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Are finite projective planes isomorphic to PG(2,q), where q=p^k with p a prime?
I can't find any reference to the following question:
Are finite projective planes isomorphic to $PG(2,q)$, where $q=p^k$ with $p$ a prime?
I think it's meaningless to continue studying without ...
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101
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Conditions under which the degree of an algebraic surface equals the degree of its planar section
An algebraic surface $\Phi$ in complex projective 3-space contains a circle $c$ such that the complex projective plane $P$ of $c$ intersects $\Phi$ only at the points of $c$. Assume that
$c$ is not a ...
- 1,488
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answers
379
views
Terminology for the image of the diagonal embedding.
Let $X$ be a topological space equipped with maps into two spaces $\bar X_1$ and $\bar X_2$. Is there a standard notation/terminology for the closure $\bar X$ in $\bar X_1 \times \bar X_2$ of the ...
- 5,359
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289
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Modular representations of the symplectic group
Let G=Sp(2m,2) be a finite symplectic group acting on $F_2^{2m}$. This group G acts 2-transitively on $\Omega_{+}$ and on $\Omega_{-}$. Let $F$ be an algebraic closure of $F_2$.
I am interested to ...
- 2,179
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303
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Automorphism group of algebraic function fields
Let $K$ be a finite field and let $F/K$ be a function field. Is it possible to deduce the genus of $F/K$ from the automorphism group of $G=Aut(F/K)$?
Is it possible to do so if we know that $|G|$ is ...
- 2,179
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253
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Online reference for bridge between $\mathbb C$ and $\mathbb F$
I am looking for a text which
1) Explains how to deduce statements about perverse sheaves on complex geometry from analogous statements in positive characteristic. For example the last chapter "De F ...
- 13.2k
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173
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What means "extended concepts of symmetry"?
Where could one find a short description oft: "two mathematical extensions of the symmetry - to moduli spaces of sheaves and to derived categories", found here? Happen there interesting
things like ...
- 10.8k
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answers
325
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Ordered Cech(-like) complexes that compute etale cohomology (of fields!)
It is well known (cf. Equivalence of ordered and unordered cech cohomology. ) that for 'usual' topologies one can compute the cohomology of sheaves either using unordered Cech complexes or ordered ...
- 16.9k
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775
views
Discrete valuation rings.
Given an algebraically closed field $\mathbb F$ of characteristic $p$, let $\mathbb A$ be a discrete valuation ring of characteristic zero having $\mathbb F$ as its residue field ( it does exist, but ...
- 1
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479
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Passage Time Distributions for Poisson processes.
Let $(X_t)_{t \geq 0}$ be a standard Poisson process with intensity $\mu$. Let $\tau_b = \inf ( t>0 : X_t= at + b)$, where $a>0$ and $b<0$, and let $\sigma = \inf (t>0 : X_t \geq at)$. ...
- 943
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212
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On 'special properties' of various 'sheaf image' functors for a local complete intersection morphism
Let $f:X\to Y$ be a local complete intersection morphism (of schemes or varieties) of (relative) dimension $c$ everywhere. Is it true that $f^!\cong f^*[2c]$ (as a functor between the derived ...
- 16.9k
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155
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General form of a symplectic map
A symplectic automorphism of a Hilbert space has the form $T=U(\cosh S+J\sinh S)$ for a unitary $U$, an antilinear involution $J$ and a positive operator $S$. In fact a version of this goes through in ...
- 1,411
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2k
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Book on linear algebraic groups in scheme language
Is there a book on linear algebraic groups using the scheme language (i.e. not Springer or Borel, but like Waterhouse, but more in-depth)?
The book should discuss topics like Borel subgroups etc.
(...
- 417
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answers
492
views
Linear Representations of the Groups
Does anyone know a good book on Linear Representations of the finite Groups which does not assumes a lot of background. Book which will be good to study for computer science and will cover all( at ...
- 81
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0
answers
352
views
Liftability in positive characteristic
What clsses of algebraic varieties over field of positive characteristic can be lift to $W_2(k)$?
- 85
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524
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DeRham cohomology
The Poincare lemma fails in positive characteristic, since pth powers vanish under differention. My question is : is there still some kind of resolution of the local system k by considering some ...
- 1
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301
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Lifting of product of a Banach algebra
Let $A$ be a non unital Banach algebra. The product induces a bounded linear map $T:A \otimes_{\gamma} A\to A$ where $\otimes_\gamma$ denotes the Banach projective tensor product.
A lifting of $T$ is ...
- 1,222
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325
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Introductory text book for Linear Recurrence Sequences
What is a good introductory text for linear recurrence sequences?
What all are the necessary prerequisite for it? (My background is in Euclidean Fourier Analysis.) After browsing through several ...
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333
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Is there a reference showing that the space $\bar{M_{g,n}}$ is a closed oriented orbifold and it is hausdorff
Is there a reference showing that the space $\bar{M_{g,n}}$ is a closed oriented orbifold and it is Hausdorff? Note: here $\bar{M_{g,n}}$ is not the Deligne-Mumford space in the usual algebraic ...
- 1,499
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206
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Vector-valued valuations on lattices
There's a fair amount of work on valuations on (modular) lattices, by which I mean functions $v : \mathcal{L} \rightarrow R$ that satisfy the modular expression
$$v(x) + v(y) = v(x \wedge y) + v(x \...
- 4,462
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1
answer
349
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Log associahedra and log noncrossing partitions--raising ops and symmetric function theory for $A_n$ (references)
Where do the following three sets $[LA]$, $[ILA]$, and $[LN]$ of partition polynomials appear in the literature?
There are two sets of partition polynomials, not in the OEIS, that serve as the ...
- 10.5k
-1
votes
1
answer
105
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What type of graph is this? (Edges that are valid / invalid depending on route to node)
I'm trying to model a questionnaire where the flow between questions depends on the answers given in previous questions.
Example. (Node represent questions, edges represent answers).
As you can see ...
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-2
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1
answer
151
views
Averaged measure in integrations
Consider
\begin{align}
& F(n,x)\equiv \int_0^x \cdots g (x_5)\int_0^{x_5} ~\int_0^{x_4} g (x_3)~~\int_0^{x_3} ~\int_0^{x_2} g (x_1)~~A(x_1)\,dx_1\cdots dx_n
\end{align}
where $g(x)$ is a measure. ...
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