Mathematics – Commutative Algebra
Scientific paper
2004-11-16
Mathematics
Commutative Algebra
64pp
Scientific paper
We associate to every equicharacteristic zero Noetherian local ring $R$ a faithfully flat ring extension which is an ultraproduct of rings of various prime characteristics, in a weakly functorial way. Since such ultraproducts carry naturally a non-standard Frobenius, we can define a new tight closure operation on $R$ by mimicking the positive characteristic functional definition of tight closure. This approach avoids the use of generalized N\'eron Desingularization and only relies on Rotthaus' result on Artin Approximation in characteristic zero. If $R$ is moreover equidimensional and universally catenary, then we can also associate to it in a canonical, weakly functorial way a balanced big Cohen-Macaulay algebra.
Aschenbrenner Matthias
Schoutens Hans
No associations
LandOfFree
Lefschetz extensions, tight closure, and big Cohen-Macaulay algebras 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 Lefschetz extensions, tight closure, and big Cohen-Macaulay algebras, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Lefschetz extensions, tight closure, and big Cohen-Macaulay algebras will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-212479