  We postulate axioms for a chiral half of a nonarchimedean 2-dimensional
bosonic conformal field theory, that is, a vertex operator algebra in which a
p-adic Banach space replaces the traditional Hilbert space. We study some
consequences of our axioms leading to the construction of various examples,
including p-adic commutative Banach rings and p-adic versions of the Virasoro,
Heisenberg, and the Moonshine module vertex operator algebras. Serre p-adic
modular forms occur naturally in some of these examples as limits of classical
1-point functions.
