The structure of locally finite varieties with polynomially many models

Abstract

We prove that a locally finite variety has at most polynomially many (in k k ) non-isomorphic k k –generated algebras if and only if it decomposes into a varietal product of an affine variety over a ring of finite representation type, and a sequence of strongly Abelian varieties equivalent to matrix powers of varieties of H H -sets, with constants, for various finite groups H H .