The defect

Details The defect The defect

2010-04-13

arxiv.org/abs/1004.2135v1

Mathematics

Commutative Algebra

43 pages

Scientific paper

We give an introduction to the valuation theoretical phenomenon of "defect", also known as "ramification deficiency". We describe the role it plays in deep open problems in positive characteristic: local uniformization (the local form of resolution of singularities), the model theory of valued fields, the structure theory of valued function fields. We give several examples of algebraic extensions with non-trivial defect. We indicate why Artin-Schreier defect extensions play a central role and describe a way to classify them. Further, we give an overview of various results about the defect that help to tame or avoid it, in particular "stability" theorems and theorems on "henselian rationality", and show how they are applied. Finally, we include a list of open problems.

Affiliated with

Also associated with

No associations

Rating

The defect 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 The defect, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The defect will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-281921