Automorphisms of Supersingular K3 Surfaces and Salem Polynomials. Issue 4 (1st October 2016)

• Record Type: Journal Article
• Authors: Shimada, Ichiro
• Is Part Of: Experimental mathematics. Volume 25:Issue 4(2016)
• Page Start: 389
• Page End: 398
• Publication Date: 2016-10-01
• Subjects: supersingular K3 surface -- automorphism -- Salem polynomial; 14J28 -- 14J50 -- 37B40 -- 14Q10; Mathematics -- Periodicals; Mathematics -- Research -- Periodicals; 510.724
• DOI: 10.1080/10586458.2015.1073641
• Languages: English
• ISSNs: 1058-6458

Abstract

Abstract: We present a method to generate many automorphisms of a supersingular K 3 surface in odd characteristic. As an application, we show that if p is an odd prime less than or equal to 7919, then every supersingular K 3 surface in characteristic p has an automorphism whose characteristic polynomial on the Néron–Severi lattice is a Salem polynomial of degree 22. For a supersingular K 3 surface with Artin invariant 10, the same holds for odd primes less than or equal to 17, 389.