Dimension and singularity theory for local rings of finite embedding dimension

Details Dimension and singularity theory for local rings of finite embedding dimension Dimension and singularity theory for local rings of finite embedding dimension

2008-09-30

arxiv.org/abs/0809.5267v1

Mathematics

Commutative Algebra

Scientific paper

In this paper, an algebraic theory for local rings of finite embedding dimension is developed. Several extensions of (Krull) dimension are proposed, which are then used to generalize singularity notions from commutative algebra. Finally, variants of the homological theorems are shown to hold in equal characteristic. This theory is then applied to Noetherian local rings in order to get: (i) over a Cohen-Macaulay local ring, uniform bounds on the Betti numbers of a Cohen-Macaulay module in terms of dimension and multiplicity, and similar bounds for the Bass numbers of a finitely generated module; (ii) a characterization for being respectively analytically unramified, analytically irreducible, unmixed, quasi-unmixed, normal, Cohen-Macaulay, pseudo-rational, or weakly F-regular in terms of certain uniform arithmetic behavior; (iii) in mixed characteristic, the Improved New Intersection Theorem when the residual characteristic or ramification index is large with respect to dimension (and some other numerical invariants).

Affiliated with

Also associated with

No associations

Rating

Dimension and singularity theory for local rings of finite embedding dimension 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 Dimension and singularity theory for local rings of finite embedding dimension, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Dimension and singularity theory for local rings of finite embedding dimension will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-253392