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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 …
Georges Elencwajg's user avatar
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 …
Martin Sleziak's user avatar
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^ …
Martin Sleziak's user avatar
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 …
Michael Hardy's user avatar
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 …
Georges Elencwajg's user avatar
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)\ …
Community's user avatar
  • 1
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 …
Danu's user avatar
  • 119
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 …
Ricardo Andrade's user avatar
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!
Georges Elencwajg's user avatar
105 votes

Not especially famous, long-open problems which anyone can understand

Is $e+\pi $ rational?
Georges Elencwajg's user avatar
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 …
Georges Elencwajg's user avatar
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 $n$.
Georges Elencwajg's user avatar
3 votes

Individual mathematical objects whose study amounts to a (sub)discipline?

$SL_2\mathbb R$ and its evil universal covering.
Georges Elencwajg's user avatar
170 votes

Most memorable titles

The flattering lie You Could Have Invented Spectral Sequences by Timothy Y. Chow.
Georges Elencwajg's user avatar
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 …
David Roberts's user avatar
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