Koszul Factorization and the Cohen-Gabber Theorem
Commutative Algebra
2017-09-26 v3 K-Theory and Homology
Abstract
We present a sharpened version of the Cohen-Gabber theorem for equicharacteristic, complete local domains (A,m,k) with algebraically closed residue field and dimension d > 0. Namely, we show that for any prime number p, Spec(A) admits a dominant, finite map to Spec(k[[X_1,...,X_d]]) with generic degree relatively prime to p. Our result follows from Gabber's original theorem, elementary Hilbert-Samuel multiplicity theory, and a "factorization" of the map induced on the Grothendieck group G_0(A) by the Koszul complex.
Cite
@article{arxiv.1610.01264,
title = {Koszul Factorization and the Cohen-Gabber Theorem},
author = {Chris Skalit},
journal= {arXiv preprint arXiv:1610.01264},
year = {2017}
}
Comments
Updated to include Journal reference and to remove minor typos