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Fall and Winter 2016 Koszul factorization and the Cohen–Gabber theorem
C. Skalit
Illinois J. Math. 60(3-4): 833-844 (Fall and Winter 2016). DOI: 10.1215/ijm/1506067294

Abstract

We present a sharpened version of the Cohen–Gabber theorem for equicharacteristic, complete local domains $(A,\mathfrak{m},k)$ with algebraically closed residue field and dimension $d>0$. Namely, we show that for any prime number $p$, $\operatorname{Spec}A$ admits a dominant, finite map to $\operatorname{Spec}k[[X_{1},\ldots,X_{d}]]$ 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 $\mathbf{G}_{0}(A)$ by the Koszul complex.

Citation

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C. Skalit. "Koszul factorization and the Cohen–Gabber theorem." Illinois J. Math. 60 (3-4) 833 - 844, Fall and Winter 2016. https://doi.org/10.1215/ijm/1506067294

Information

Received: 20 October 2016; Revised: 7 April 2017; Published: Fall and Winter 2016
First available in Project Euclid: 22 September 2017

zbMATH: 1376.13011
MathSciNet: MR3705447
Digital Object Identifier: 10.1215/ijm/1506067294

Subjects:
Primary: 13D40, 13H15, 19A49

Rights: Copyright © 2016 University of Illinois at Urbana-Champaign

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Vol.60 • No. 3-4 • Fall and Winter 2016
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