  I coined the term anabelomorphy (pronounced as anabel-o-morphy) as a concise
way of expressing Mochizuki's idea of "anabelian way of changing ground field,
rings etc." which was he has introduced in his work on his Inter-Universal
Teichmuller Theory. This paper demonstrates the usefulness of this idea by
studying its ramifications in the more familiar arithmetic contexts such as the
theory of Galois representations, automorphic forms and related areas and
establish a number of results which are of independent arithmetic interest. I
also introduce the notion of anabelomorphically connected number fields in
which two number fields are related by the existence of topological isomorphism
between the local Galois groups at a finite list of primes of both the number
fields and prove some results illustrating arithmetic consequences of this
notion. The Introduction provides a detailed discussion and summary of all the
results proved in this paper.
