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Results tagged with big-list
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Questions designed to generate a "big list" of certain results, examples, conjectures, etc. via many individual answers, each contributing one or a few instances. Such a question should typically be in Community Wiki mode (CW); after asking, please, flag for moderators attention requesting the question to be made CW.
10
votes
Any reference on multilinear algebra
Here are three excellent books.
Tensor Spaces and Exterior Algebra by Takeo Yokonuma.
Translations of Mathematical Monographs, volume 108, AMS 1992
You can browse it in Google books here
Laurent Sc …
159
votes
What are some examples of colorful language in serious mathematics papers?
Andre Weil (Oeuvres, vol. 2, page 558) purporting to be R.Lipschitz writing from Hades:
"Unfortunately, it appears that there is now in your world a race of
vampires, called referees, who clamp down m …
73
votes
Accepted
Cardinalities larger than the continuum in areas besides set theory
The Zariski tangent space at any point of a positive dimensional $C^1$-manifold $X$ has dimension $2^{2^{\aleph_0}}= 2^{\frak c}$.
Let me explain in the case when $X=\mathbb R$.
Consider the ring $C^ …
2
votes
Interesting examples of vacuous / void entities
A The empty set is a covering map of any topological space. More generally, a covering map needn't be surjective (although many books claim just that). For example the inclusion of a closed and open …
43
votes
What should be learned in a first serious schemes course?
Since in 2007-2008 you evoked [ Class 24, §1.8, The problem with locally free sheaves] the equivalence between locally free sheaves and vector bundles on a scheme, the following point, potentially co …
70
votes
What elementary problems can you solve with schemes?
If $I,J \subset A$ are comaximal ideals in a commutative ring $A$, i.e. $I+J=A$, then
for all $n,m \in \mathbb N$ the ideals $I^n$ and $J^m$ are also comaximal.
Proof: $\emptyset= V(A)=V(I+J)=V(I)\ …
53
votes
Pseudonyms of famous mathematicians
Rainich=Rabinowitsch (of trick fame : cf. Nullstellensatz).
Here is an anecdote related by Bruce P. Palka, Editor of American Mathematical Monthly
in Vol.111 (2004) of that journal (page460).
Rai …
14
votes
Fundamental Examples
In the theory of holomorphic functions of several variables, Hartogs's theorem that any holomorphic function on a punctured open set of $\mathbb C^n$ ($n\geqslant 2$) can holomorphically be continued …
52
votes
Fundamental problems whose solution seems completely out of reach
Is every algebraic curve in $\mathbb P^3$ the set-theoretic intersection of two algebraic surfaces ? Not known!
105
votes
Not especially famous, long-open problems which anyone can understand
Is $e+\pi $ rational?
7
votes
Examples of naturally occurring Quadratic forms or quadrics.
Dear Olivier, in line with the more advanced nature of this site, let me give an example of a less elementary nature.
Consider a compact Riemann surface $X$ of genus 2 and on it stable vector bundles …
44
votes
Theorems that are 'obvious' but hard to prove
That $\mathbb R^n$ has topological dimension $n$. In a similar vein that affine space $\mathbb A^n_k$ over a field $k$ has Zariski dimension $n$.
3
votes
Individual mathematical objects whose study amounts to a (sub)discipline?
$SL_2\mathbb R$ and its evil universal covering.
170
votes
Most memorable titles
The flattering lie You Could Have Invented Spectral Sequences by Timothy Y. Chow.
16
votes
Proof synopsis collection
Fermat's little theorem: $n^p\equiv n \; (mod \;p)$ for $p$ prime and all integers $n$.
Synopsis of proof: Reduce to nontrivial case where $p$ doesn't divide $n$, interpret as equality in field of $p …