  For a split reductive group defined over a number field, we first introduce
the notations of arithmetic torsors and arithmetic Higgs torsors. Then we
construct arithmetic characteristic curves associated to arithmetic Higgs
torsors, based on the Chevalley characteristic morphism and the existence of
Chevalley basis for the associated Lie algebra. As to be expected, this work is
motivated by the works of Beauville-Narasimhan on spectral curves and
Donagi-Gaistgory on cameral curves in algebraic geometry. In the forthcoming
papers, we will use arithmetic characteristic curves to construct arithmetic
Hitchin fibrations and study the intersection homologies and perverse sheaves
for the associated structures, following Ngo's approach to the fundamental
lemma.
