Isometries of lattices and Hasse principles

2020/01/20 by Bayer-Fluckiger, Eva · 2 citations
#FOS: Mathematics #Geometric Topology (math.GT) #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2001.07094

Abstract

We give necessary and sufficient conditions for an integral polynomial without linear factors to be the characteristic polynomial of an isometry of some even, unimodular lattice of given signature. This gives rise to Hasse principle questions, which we answer in a more general setting. As an application, we prove a Hasse principle for signatures of knots.

Cited by

• Non-projective K3 surfaces with real or Salem multiplication
• On Salem numbers of degree 4 and arithmetic hyperbolic orbifolds

Related

• Characteristic polynomials of isometries of even unimodular lattices
• Isometries of lattices and automorphisms of K3 surfaces
• Automorphisms of even unimodular lattices and equivariant Witt groups
• Lattice isometries and K3 surface automorphisms: Salem numbers of degree 20
• Why the characteristic polynomial factors