Covers of rational double points in mixed characteristic

Journal of Singularities
volume 23 (2021), 127-150

Received: 5 March 2021. Received in revised form: 19 July 2021.

DOI: 10.5427/jsing.2021.23h

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Abstract:

We further the classification of rational surface singularities. Suppose (S, n, k) is a 3-dimensional strictly Henselian regular local ring of mixed characteristic (0, p>5). We classify functions f for which S/(f) has an isolated rational singularity at the maximal ideal n. The classification of such functions are used to show that if (R, m, k) is an excellent, strictly Henselian, Gorenstein rational singularity of dimension 2 and mixed characteristic (0, p>5), then there exists a split finite cover of Spec(R) by a regular scheme. We give an application of our result to the study of 2-dimensional BCM-regular singularities in mixed characteristic.

Author(s) information:

Javier Carvajal-Rojas
École Polytechnique Fédérale de Lausanne
SB MATH CAG, MA C3 615 (Bâtiment MA)
Station 8
CH-1015 Lausanne, Switzerland
email: javier.carvajalrojas@epfl.ch

Linquan Ma
Department of Mathematics
Purdue University
West Lafayette, IN 47907, USA
email: ma326@purdue.edu

Thomas Polstra
Department of Mathematics
University of Virginia
Charlottesville, VA 22903, USA
email: tp2tt@virginia.edu

Karl Schwede
Department of Mathematics
University of Utah
Salt Lake City, UT 84112, USA
email: schwede@math.utah.edu

Kevin Tucker
Department of Mathematics
University of Illinois at Chicago
Chicago, IL 60607, USA
email: kftucker@uic.edu