Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2401.13508

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

Kirti Joshi
View original source ↗Read source document ↗Export metadata ↓

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 §12.

Explore related subjects

math.AGmath.NT

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Kirti Joshi. 2025-02-24. Construction of Arithmetic Teichmuller Spaces III: A `Rosetta Stone' and a proof of Mochizuki's Corollary 3.12. https://arxiv.org/abs/2401.13508

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

G3-Criteria and Applications

The G3-property of a subvariety was introduced by Hironaka-Matsumura, and plays an important role for deducing connectedness and extension results. Unfortunately, it's a rather elusive notion, which is not always easy to establish. Most of the existing work is concentrated on subvarieties of homogeneous varieties. The first goal of this article is to show that mobility assumptions on the subvariety, considered in works of Badescu, Chow, Debarre, Voisin, yield a certain partial positivity property, slightly stronger than G3, previously introduced by the author. Second, we apply the result to prove that, in numerous situations, the splitting of the normal bundle of a smooth two-codimensional subvariety implies that it is a complete intersection.

math.AG↗
arXiv2026

Nodal degeneration of chiral algebras I: Global structure and gluing formula

We define a natural extension of a universal factorization algebra $\mathcal{A}$ to families of stable punctured curves, by integrating over all semistable modifications. We prove that the resulting sheaf of factorization homology satisfies a natural gluing formula, by tensoring over a certain derived associative algebra $\mathfrak{Z}_{\mathcal{A}}^0$, generalizing the Verlinde formula for gluing of conformal blocks.

math.AG↗