Timeline for "Cute" applications of the étale fundamental group
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 1, 2021 at 22:34 | comment | added | Martin Brandenburg | ... and also at this wonderful mathoverflow thread: mathoverflow.net/questions/45951/… | |
| Jul 1, 2021 at 22:28 | comment | added | Martin Brandenburg | The "definition" restricts to non-empty open subsets (at least in my edition), which then also implies that the sheaf condition only applies to covers with non-empty intersections. In particular, $F(U \sqcup V) = F(U) \times F(V)$ may fail with that "definition". There is a general theme in mathematics that some authors want to "simplify" the definitions by omitting "non-interesting" cases (e.g. to define Banach algebras to be non-trivial, or graphs to be non-empty), which is a mistake; a long elaboration can be found here. | |
| Jul 1, 2021 at 19:06 | comment | added | Gabriel | @MartinBrandenburg having read it from the first to the last page, I agree that it has some inaccuracies, mainly because the author tries to do "an exposition" of some hard stuff to people that don't yet have the needed background. That doesn't always works (who can learn scheme theory in less than 10 pages, for example?) but this book has some stuff that is hard to find in elsewhere. (But what is the problem with its definition of a sheaf btw?) | |
| Jul 1, 2021 at 10:16 | comment | added | Martin Brandenburg | I cannot recommend the mentioned book "Galois Groups and Fundamental Groups", though. It contains several inaccuracies, and most notably the definition of a sheaf is wrong (not just inaccurate). | |
| Mar 10, 2021 at 14:23 | history | answered | Gabriel | CC BY-SA 4.0 |