We would like to give a kind of brief survey on the theory of supersingular abelian varieties and arithmetic theory of quaterion hermitian lattices, emphasizing the latter. Two theories are very closely related.
Many of important invariants of supersingular abelian varieties are expressed by arithmetic invariants of lattices.We roughly sketch without proof what are known for the arithmetic theory of lattices,including class number formula, type number formula and automorphisms.
We also give their counter part for invariants of supersingular or superspecial abelian varieties or rational points of curves over finite fields related with coding theory and explain how these two kinds of objects match together.
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