# Construction of Arithmetic Teichmuller spaces II: Towards Diophantine Estimates

@inproceedings{Joshi2021ConstructionOA, title={Construction of Arithmetic Teichmuller spaces II: Towards Diophantine Estimates}, author={Kirti Joshi}, year={2021} }

This paper deals with three consequences of the existence of Arithmetic Teichmuller spaces of arXiv:2106.11452. Let $\mathscr{X}_{F,\mathbb{Q}_p}$ (resp. $B=B_{\mathbb{Q}_p}$) be the complete Fargues-Fontaine curve (resp. the ring) constructed by Fargues-Fontaine with the datum $F={\mathbb{C}_p^\flat}$ (the tilt of $\mathbb{C}_p$), $E=\mathbb{Q}_p$. Fix an odd prime $\ell$, let $\ell^*=\frac{\ell-1}{2}$. The construction (\S 7) of an uncountable subset $\Sigma_{F}\subset \mathscr{X}_{F,\mathbb…

## References

SHOWING 1-10 OF 24 REFERENCES

### A Proof of the ABC Conjecture

- Philosophy
- 2014

We first get rid of three kinds from A+B=C according to their respective odevity and gcf (A, B, C) =1. After that, expound relations between C and raf (ABC) by the symmetric law of odd numbers.…

### ISSN 0303-1179. With a preface by Pierre Colmez

- Courbes et fibrés vectoriels en théorie de Hodge p-adique. Astérisque,
- 2018

### The mathematics of mutually alien copies: from gaussian integrals to inter-universal teichmüller theory

- 2020

### Construction of Arithmetic Teichmuller Spaces and some applications

- Mathematics
- 2021

In this note I construct some categories which can be called Arithmetic Teichmuller Spaces. This construction is very broadly inspired by Shinichi Mochizuki's ideas on Anabelian Geometry, p-adic…

### The Statement of Mochizuki's Corollary 3.12, Initial Theta Data, and the First Two Indeterminacies

- Mathematics
- 2020

This paper does not give a proof of Mochizuki's Corollary 3.12. It is the first in a series of three papers concerning Mochizuki's Inequalities. The present paper concerns the setup of Corollary 3.12…

### Probabilistic Szpiro, Baby Szpiro, and Explicit Szpiro from Mochizuki's Corollary 3.12

- Mathematics
- 2020

In \cite{Dupuy2020a} we gave some explicit formulas for the "indeterminacies" Ind1,Ind2,Ind3 in Mochizuki's Inequality as well as a new presentation of initial theta data. In the present paper we use…

### TOPICS IN ABSOLUTE ANABELIAN GEOMETRY III: GLOBAL RECONSTRUCTION ALGORITHMS

- Mathematics
- 2015

In the present paper, which forms the third part of a three-part series on an algorithmic approach to absolute anabelian geometry, we apply the ab- solute anabelian technique of Belyi cuspidalization…

### Inter-universal Teichmüller Theory III: Canonical Splittings of the Log-Theta-Lattice

- Mathematics
- 2021

The present paper constitutes the third paper in a series of four papers and may be regarded as the culmination of the abstract conceptual portion of the theory developed in the series. In the…

### Inter-universal Teichmüller Theory II: Hodge–Arakelov-Theoretic Evaluation

- Mathematics
- 2021

In the present paper, which is the second in a series of four papers, we study theKummer theory surrounding the Hodge-Arakelov-theoretic evaluation — i.e., evaluation in the style of the…

### Topics in Absolute Anabelian Geometry I: Generalities

- Mathematics
- 2012

This paper forms the first part of a three-part series in which we treat various topics in absolute anabelian geometry from the point of view of developing abstract algorithms ,o r"software", that…