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Results tagged with intuition
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user 450
Questions asking for the intuition behind some definition, conjecture, proof etc. In other words, questions designed to improve or to acquire understanding on a conceptual or intuitive level, as opposed to on a technical or formal level. When asking such a question it can be helpful to include a rough description of ones understanding of the subject at hand (on a technical level).
35
votes
Accepted
A geometric characterization for arithmetic genus
First let me note that there is an unfortunate clash in terminology: the arithmetic genus of a smooth complex projective variety $X$ of dimension $n$ can mean either
a) The number $\chi (X, \mathca …
- 47.5k
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 …
61
votes
Intuition for Group Cohomology
Here is a completely elementary example which shows that group cohomology is not empty verbiage, but can solve a problem ("parametrization of rational circle") whose statement has nothing to do with c …
- 47.5k
5
votes
Most helpful heuristic?
Dear harrison,
in complex geometry there is Oka's principle.
It says that on a stein manifold, if there is no obstruction to a continuous construction there will be no obstruction to a holomorphic c …