# Questions tagged [reference-request]

This tag is used if a reference is needed in a paper or textbook on a specific result.

9,619 questions

**2**

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### Denominator identity for Lie superalgebras

Let $\mathfrak g$ be a basic classic simple Lie superalgebra.
Fix a maximal isotropic subset $S \subset \Delta$ and choose a set of simple roots $\Pi$ containing $S$. Let $R$ be the Weyl ...

**7**

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55 views

### Monadic second-order theories of the reals

I’m looking for a survey of monadic second-order theories of the reals.
I’m starting from a 1985 survey by Gurevich which says (p 505) that true arithmetic can be reduced to “the monadic theory of ...

**5**

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104 views

### Original reference for Adams-Riemann-Roch theorem

Let $f\colon Y\to X$ be a proper morphism between smooth quasiprojective $k$-algebraic varieties. Denote $\psi^j$ the $j$-th Adams operation on the Grothendieck group of vector bundles and $\theta^j(...

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71 views

### Unramified local Langlands

Where can I find a complete proof of the unramified local Langlands correspondence for arbitrary reductive groups? Second sentence included because the automated system would not accept my question.

**3**

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**1**answer

120 views

### Cohomogy of local systems over CW-complexes

Let $M$ be a finite CW-complex. Let $F$ be a finite rank local system over $M$ with coefficients in any field. Is it true that $\dim(H^k(M,F))$ is at most the number of $k$-cells times $\operatorname{...

**4**

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195 views

### Do we know what the impulse to “introduce” the Jordan canonical form was?

Mo-ers,
Do you know how it was that the study of the Jordan canonical form began?
There are certain things that may be said once one has thought about the matter: for instance, one can say that the ...

**1**

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**0**answers

24 views

### Dynkin diagram of Basic classical simple Lie superalgebras

Let $\mathfrak g = \mathfrak g_0 \oplus \mathfrak g_1$ be a basic classical simple Lie superalgebra with the root system $\Delta = \Delta_0 \cup \Delta_1$ and Dynkin diagram $\Gamma$. It is well-known ...

**2**

votes

**1**answer

50 views

### Reference request: When is the variance in the central limit theorem for Markov chains positive?

I'm looking for a reference which gives sufficient conditions for the variance to be positive in the central limit theorem for Markov chains (cf https://en.wikipedia.org/wiki/...

**4**

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215 views

### Rationally connected Kähler manifolds are projective

I would like to find a proof for Remark 0.5 in the following article of Claire Voisin:
https://webusers.imj-prg.fr/~claire.voisin/Articlesweb/fanosymp.pdf
She writes in this remark the following:
...

**-1**

votes

**2**answers

127 views

### Directed colimit and homology

I am looking for a reference or a proof of the following fact:
Let $X_{1}\subset X_{2}\subset\dots $ be a sequence of (hausdorff) topological spaces indexed by natural numbers such that each $X_{i}\...

**3**

votes

**1**answer

116 views

### A pair of spaces equivalent to a pair of CW-complexes

Suppose that $X$ is a CW-complex and $Y$ a CW-subcomplex of $X$. Let $A$ be a closed subspace of $Z$ such that
$Z-A$ is homeomorhic to $X-Y$ and
$Z/A$ homeomorphic to $X/Y$ and
The closure of $Z-A$ ...

**-1**

votes

**1**answer

70 views

### Reference Request: Carnot Group Not Containing Group of Isometries

This question is a follow-up to this post, from which I quote:
Let $\mathfrak{e}$ be the 3-dimensional Lie algebra with basis $(H,X,Y)$ and bracket $[H,X]=Y$, $[H,Y]=-X$, $[X,Y]=0$. It is ...

**5**

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105 views

### Closed embedding of CW-complexes

Suppose that $i: X\rightarrow Y$ is a closed embedding such that $X$ and $Y $ are (retracts) of CW-complexes. Does it follow that $i$ is a cofibration ?
Remark: There is a similar question here, ...

**5**

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46 views

### Functional Equation of Zeta Function on Statistical Model

I've been studying [1] because I was interested in his ideas on the zeta function. I'll define it here (c.f. p. 31):
The Kullback-Leibler distance is defined as
$$
K(w)=\int q(x)f(x, w)dx\quad
f(x,w)...

**0**

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158 views

### Good texts (other than Kunen and Jech) on set theory, specifically on consistency proofs (reflection theorems, absoluteness, etc) [on hold]

I'm finding Kunen and Jech bit of a hard read, and cannot seem to find good alternatives. Please suggest.