Geometric Auslander criterion for flatness

Details Geometric Auslander criterion for flatness Geometric Auslander criterion for flatness

2009-01-18

arxiv.org/abs/0901.2744v4

Mathematics

Commutative Algebra

15 pages; to appear in American Journal of Mathematics

Scientific paper

We prove that, if F is a coherent sheaf of modules over the source of a morphism f:X->Y of complex-analytic spaces, where Y is smooth, then the stalk of F at a point x in X is flat over R, the local ring of the target at f(x) if and only if the n-fold analytic tensor power of this stalk over R (where n = dim R) has no vertical elements. The result implies that if F is a finite module over a morphism f:X->Y of complex algebraic varieties, where Y is smooth and n=dim Y, then the stalk of F at x is R-flat if and only if its n-fold tensor power is a torsionfree R-module. The latter generalizes a classical freeness criterion of Auslander to modules that are not necessarily finitely generated over the base ring.

Affiliated with

Also associated with

No associations

Rating

Geometric Auslander criterion for flatness 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 Geometric Auslander criterion for flatness, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Geometric Auslander criterion for flatness will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-566119