Construction of Arithmetic Teichmuller Spaces III: A `Rosetta Stone' and a proof of Mochizuki's Corollary 3.12

Abstract: This is a continuation of my work on Arithmetic Teichmuller Spaces (arXiv:2106.11452, arXiv:2210.11635, arXiv:2303.01662, arXiv:2305.10398). This paper establishes a number of important results including (1) a proof Mochizuki's Corollary 3.12 (2) establishes a `Rosetta Stone' for a parallel reading of Mochizuki's Inter-Universal Teichmuller Theory and my Theory of Arithmetic Teichmuller Spaces, and (3) a proof that Mochizuki's gluing of Hodge-Theaters, Frobenioids along prime-strips as described in his theory is naturally provided by the existence of Arithmetic Teichmuller Spaces. (4) Includes the geometric case of Mochizuki's Corollary 3.12 in \S 12.