20/04/05 09:46:40.97 cTzpxuVq.net
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URLﾘﾝｸ(arxiv.org)
On Mochizuki’s idea of Anabelomorphy and its applications Kirti Joshi 20200305
26 Perfectoid algebraic geometry as an example of anabelomorphy
A detailed treatment of assertions of this section will be provided in [DJ] where we establish many results in parallel with classical anabelian geometry.
In some sense Scholze’s proof of the weight monodromy conjecture does precisely this: Scholze replaces the original hypersurface by a (perfectoid) nabelomorphic hypersurface for which the conjecture can be established by other means.
＜References＞
[DJ] Taylor Dupuy and Kirti Joshi. Perfectoid anbelomorphy.
[DHa] Taylor Dupuy and Anton Hilado. Probabilitic Szpiro, baby Szpiro, and
explicit Szpiro from Mochizuki’s corollary 3.12. Preprint.
URLﾘﾝｸ(www.uvm.edu) Taylor Dupuy's Homepage manuscripts
2. Probabilistic Szpiro, Baby Szpiro, and Explicit Szpiro from Mochizuki's Corollary 3.12, (with A. Hilado)
URLﾘﾝｸ(www.dropbox.com)
PROBABILISTIC SZPIRO, BABY SZPIRO, AND EXPLICIT SZPIRO
FROM MOCHIZUKI'S COROLLARY 3.12
DRAFT
TAYLOR DUPUY AND ANTON HILADO Date: April 4, 2020.
Abstract. In [DH19] 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 these explicit formulas, together with our probabilistic formulation of [Moc15a,
Corollary 3.12] to derive variants of Szpiro's inequality (in the spirit of [Moc15b]). In particular,
for an elliptic curves in initial theta data we show how to derive uniform Szpiro
(with explicit numerical constants). The inequalities we get will be strictly weaker than
[Moc15b, Theorem 1.10] but the proofs are more transparent, modifiable, and user friendly.
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