Vol. 319, No. 1, 2022

Download this article
Download this article For screen
For printing
Recent Issues
Vol. 328: 1  2
Vol. 327: 1  2
Vol. 326: 1  2
Vol. 325: 1  2
Vol. 324: 1  2
Vol. 323: 1  2
Vol. 322: 1  2
Vol. 321: 1  2
Online Archive
The Journal
Editorial Board
Submission Guidelines
Submission Form
Policies for Authors
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Special Issues
Author Index
To Appear
Other MSP Journals
This article is available for purchase or by subscription. See below.
Rigidity of valuative trees under henselization

Enric Nart

Vol. 319 (2022), No. 1, 189–211

Let (K,v) be a valued field and let (Kh,vh) be the henselization determined by the choice of an extension of v to an algebraic closure of K. Consider an embedding v(K)Λ of the value group into a divisible ordered abelian group. Let 𝒯 (K,Λ), 𝒯 (Kh,Λ) be the trees formed by all Λ-valued extensions of v, vh to the polynomial rings K[x], Kh[x], respectively. We show that the natural restriction mapping 𝒯 (Kh,Λ) 𝒯 (K,Λ) is an isomorphism of posets.

As a consequence, the restriction mapping 𝒯vh 𝒯v is an isomorphism of posets too, where 𝒯v, 𝒯vh are the trees whose nodes are the equivalence classes of valuations on K[x], Kh[x] whose restrictions to K, Kh are equivalent to v, vh, respectively.

PDF Access Denied

We have not been able to recognize your IP address as that of a subscriber to this journal.
Online access to the content of recent issues is by subscription, or purchase of single articles.

Please contact your institution's librarian suggesting a subscription, for example by using our journal-recom­mendation form. Or, visit our subscription page for instructions on purchasing a subscription.

You may also contact us at contact@msp.org
or by using our contact form.

Or, you may purchase this single article for USD 40.00:

henselization, key polynomial, valuation, valuative tree
Mathematical Subject Classification
Primary: 13A18
Secondary: 12J20, 13J10, 14E15
Received: 4 February 2022
Revised: 15 April 2022
Accepted: 16 April 2022
Published: 28 August 2022
Enric Nart
Departament de Matemàtiques
Universitat Autònoma de Barcelona
Cerdanyola del Vallès