• Corpus ID: 243860921

# 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

• 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
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
• 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
• 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
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
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
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
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