Timeline for Is an algebraic geometer's fibration also an algebraic topologist's fibration?
Current License: CC BY-SA 2.5
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 27, 2010 at 15:42 | vote | accept | HYYY | ||
| Jun 15, 2010 at 13:11 | comment | added | Tim Perutz | Andrew, fair enough - I read HYYY's comment as confirming my interpretation, which was initially just a hunch. I could have misinterpreted the comment as well as the question. I don't propose to bump the question by editing my answer, but HYYY should edit his/her question! | |
| Jun 15, 2010 at 6:18 | comment | added | Andrew Stacey | I'm baffled by the statement: "Now that the intent of the question has become clear"! It's certainly not clear to me. The one addendum by the original questioner seems to imply that the question is about algebraic topology not geometry, so I don't understand either the retagging or the algebraic geometrical answer. | |
| Jun 15, 2010 at 2:12 | comment | added | Boyarsky | Grothendieck's descent theory allows one to treat faithfully flat quasi-compact (fpqc) maps "as if" they're topological fibrations. Lots of theorems say "the locus of points in the base when property P holds is open" for a proper fppf (faithfully flat, finitely presented) map, and fibral properties often imply relative properties (e.g., smooth morphisms) for fppf maps. In the algebro-geometric study of torsors for group schemes, fppf-local (or etale-local) sections are a good notion of "local triviality". So the word "fibration" for fppf map (especially in the proper case) is appropriate. | |
| Jun 15, 2010 at 2:02 | comment | added | Tim Perutz | Unwanted adjectives get dropped, things become ambiguous... So, long ago they played association football and Rugby football, and then (I suppose) the US version seemed close enough to Rugby football for American football to make sense as a name. But then two adjectives plus one noun get dropped, and we're left with two footballs plus one English public (that is, private) school... And it all made sense at the time. | |
| Jun 15, 2010 at 0:47 | comment | added | Ryan Budney | How did algebraic geometers come to adopt "fibration" as an article of terminology? At some point someone must have been concerned about re-use of the same term. | |
| Jun 15, 2010 at 0:34 | history | answered | Tim Perutz | CC BY-SA 2.5 |