Flatness testing over singular bases

Details Flatness testing over singular bases Flatness testing over singular bases

2011-09-16

arxiv.org/abs/1109.3738v1

Mathematics

Commutative Algebra

8 pages

Scientific paper

We show that non-flatness of a morphism f of complex-analytic spaces with a locally irreducible target Y of dimension n manifests in the existence of vertical components in the n-fold fibred power of the pull-back of f to the desingularization of Y. An algebraic analogue follows: Let R be a locally (analytically) irreducible finite type complex-algebra and an integral domain of Krull dimension n, and let S be a regular n-dimensional algebra of finite type over R (but not necessarily a finite R-module), such that the induced morphism of spectra is dominant. Then a finite type R-algebra A is R-flat if and only if the tensor product of S with the n-fold tensor power of A over R is a torsion-free R-module.

Affiliated with

Also associated with

No associations

Rating

Flatness testing over singular bases does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Flatness testing over singular bases, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Flatness testing over singular bases will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-142193