The distance between superspecial abelian varieties with real multiplication (Q1019858)

The minimal degree of an isogeny between two elliptic curves is referred to the distance between them in analogy with the terminology of graphs. In this paper, upper and lower bounds of the distance between superspecial abelian varieties with real multiplication are proposed. Concretely, for ``\(L\)'' a real field of strict class number one and for ``\(p\)'' a prime unramified in \(L\), the degree of an isogeny between two superspecial abelian varieties with real multiplication by \(L\) in characteristic \(p\) is a positive element of its ring of integers.