Translator Disclaimer
15 May 2018 The critical height is a moduli height
Patrick Ingram
Duke Math. J. 167(7): 1311-1346 (15 May 2018). DOI: 10.1215/00127094-2017-0053

Abstract

Silverman defined the critical height of a rational function f(z) of degree d2 in terms of the asymptotic rate of growth of the Weil height along the critical orbits of f. He also conjectured that this quantity was commensurate to an ample Weil height on the moduli space of rational functions degree d. We prove that conjecture.

Citation

Download Citation

Patrick Ingram. "The critical height is a moduli height." Duke Math. J. 167 (7) 1311 - 1346, 15 May 2018. https://doi.org/10.1215/00127094-2017-0053

Information

Received: 10 January 2017; Revised: 15 October 2017; Published: 15 May 2018
First available in Project Euclid: 3 March 2018

zbMATH: 06892360
MathSciNet: MR3799700
Digital Object Identifier: 10.1215/00127094-2017-0053

Subjects:
Primary: 37P30
Secondary: 11G50

Rights: Copyright © 2018 Duke University Press

JOURNAL ARTICLE
36 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.167 • No. 7 • 15 May 2018
Back to Top