  Let $p$ be a prime number. Let $X/E$ be a geometrically connected, smooth,
quasi-projective variety over a finite extension $E/\mathbb{Q}_p$. In this
paper I demonstrate the existence of isomorphs of the tempered (and hence also
\'etale) fundamental group of $X/E$ which are labeled by distinct arithmetic
holomorphic structures, just as isomorphs of the fundamental group of a Riemann
surface $\Sigma$ may be labeled by Riemann surfaces (i.e. complex holomorphic
structures) $\Sigma'$ in the Teichmuller space of $\Sigma$. This is the
starting point of the theory elaborated in [Joshi, 2021a,b,c, 2022] for which
this paper is intended as an brief sketch and announcement. Arithmetic
holomorphic structures introduced here also provide distinct arithmetic
holomorphic structures used by Shinichi Mochizuki in [Mochizuki,2021a,b,c,d].
Since the question of whether or not there exists distinct arith. hol.
structures in [Mochizuki,2021a,b,c,d] was raised in [Scholze and Stix], I
include a discussion of [Scholze and Stix]. See the introduction for additional
details.
