Search Results
| Search type | Search syntax |
|---|---|
| Tags | [tag] |
| Exact | "words here" |
| Author |
user:1234 user:me (yours) |
| Score |
score:3 (3+) score:0 (none) |
| Answers |
answers:3 (3+) answers:0 (none) isaccepted:yes hasaccepted:no inquestion:1234 |
| Views | views:250 |
| Code | code:"if (foo != bar)" |
| Sections |
title:apples body:"apples oranges" |
| URL | url:"*.example.com" |
| Saves | in:saves |
| Status |
closed:yes duplicate:no migrated:no wiki:no |
| Types |
is:question is:answer |
| Exclude |
-[tag] -apples |
| For more details on advanced search visit our help page | |
Results tagged with big-list
Search options answers only
not deleted
user 450
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.
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?
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)\ …
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.
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 …
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 …
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^ …
- 47.5k
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 …
48
votes
Errata for Atiyah–Macdonald
Dear Tim, on page 31 they consider a ring $A$ and two $A$- algebras defined by their structural ring morphisms $f:A\to B$ and $g:A\to C$. They then define the tensor product as a ring $D=B\otimes _A C …
88
votes
Widely accepted mathematical results that were later shown to be wrong?
In 1882 Kronecker proved that every algebraic subset in $\mathbb P^n$ can be cut out by $n+1$ polynomial equations.
In 1891 Vahlen asserted that the result was best possible by exhibiting
a curve in …
13
votes
What should be learned in a first serious schemes course?
If you decide to teach a more arithmetically flavoured algebraic geometry, students should be made aware that schemes over a ring $A$ are stranger than they might think.
For example $A$-rational poin …
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 …