Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911

   
 
 

 

Elliptic $ K3$ surfaces with $ {\mathbf p}^{\mathbf n}$-torsion sections


Authors: Hiroyuki Ito and Christian Liedtke
Journal: J. Algebraic Geom. 22 (2013), 105-139
DOI: https://doi.org/10.1090/S1056-3911-2012-00584-0
Published electronically: March 14, 2012
MathSciNet review: 2993049
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Abstract: We classify elliptic K3 surfaces in characteristic $ p$ with $ p^n$-torsion section. For $ p^n\geq 3$ we verify conjectures of Artin and Shioda, compute the heights of their formal Brauer groups, as well as Artin invariants and Mordell-Weil groups in the supersingular cases.


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Hiroyuki Ito
Affiliation: Department of Applied Mathematics, Graduate School of Engineering, Hiroshima University, Higashi-Hiroshima 739-8527, Japan
Address at time of publication: Department of Mathematics, Faculty of Science and Technology, Tokyo University of Science, 2641 Yamazaki, Noda, Chiba, 278-8510, Japan
Email: hiroito@amath.hiroshima-u.ac.jp ito{\textunderscore}hiroyuki@ma.noda.tus.ac.jp

Christian Liedtke
Affiliation: Department of Mathematics, Stanford University, 450 Serra Mall, Stanford, California 94305-2125
Address at time of publication: Mathematisches Institut, Universität Bonn, Endenicher Allee 60, 53115 Bonn, Germany
Email: liedtke@math.stanford.edu

DOI: https://doi.org/10.1090/S1056-3911-2012-00584-0
Received by editor(s): April 16, 2010
Received by editor(s) in revised form: December 3, 2010, and January 3, 2011
Published electronically: March 14, 2012
Additional Notes: The first author acknowledges the support by Grant-in-Aid for Scientific Research (C) 20540044, the Ministry of Education, Culture, Sports, Science and Technology. The second author gratefully acknowledges funding from DFG under research grant LI 1906/1-1 and thanks the Department of Mathematics at Stanford University for kind hospitality.

American Mathematical Society