Timeline for Does the free resolution of the cokernel of a generic matrix remain exact on a Zariski open set?
Current License: CC BY-SA 2.5
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| Jun 13, 2010 at 17:24 | vote | accept | Jesse Burke | ||
| Jun 13, 2010 at 4:09 | comment | added | BCnrd | So yes, it is the question you meant to ask. A finite collection of polynomials with indeterminate coefficients is parameterized by a big affine space, and at the generic point the coefficients are true indeterminates (whereas at the origin the polys are all zero, etc.). Working over a dense open in this affine space is precisely considering coefficients avoiding some nontrivial algebraic relations. There's a huge development in EGA IV3 showing how results at a generic fiber imply results over dense opens (thereby "justifying" the name "generic point"). | |
| Jun 13, 2010 at 2:43 | comment | added | Jesse Burke | I don't think that's the question I meant to ask. I used generic in a different sense: take polynomials with coefficients in a field and replace those coefficients with new variables. I think one of the problems that I'm having is that I don't see how generic in that sense relates to the notion of generic point of a scheme. | |
| Jun 13, 2010 at 1:38 | history | answered | Boyarsky | CC BY-SA 2.5 |