Publication
Title
Nonsplit conics in the reduction of an arithmetic curve
Author
Abstract
For a function field in one variable F/ K and a discrete valuation v of K with perfect residue field k, we bound the number of discrete valuations on F extending v whose residue fields are non-ruled function fields in one variable over k. Assuming that K is relatively algebraically closed in F, we find that the number of non-ruled residually transcendental extensions of v to F is bounded by g + 1 where g is the genus of F/ K. An application to sums of squares in function fields of curves over R((t)) is outlined.
Language
English
Source (journal)
Mathematische Zeitschrift. - Berlin, 1918, currens
Publication
Berlin : 2024
ISSN
0025-5874 [print]
1432-1823 [online]
DOI
10.1007/S00209-023-03395-3
Volume/pages
306 :1 (2024) , p. 1-16
Article Reference
12
ISI
001114308100001
Full text (Publisher's DOI)
Full text (open access)
The author-created version that incorporates referee comments and is the accepted for publication version Available from 05.06.2024
Full text (publisher's version - intranet only)
UAntwerpen
Faculty/Department
Research group
Publication type
Subject
Affiliation
Publications with a UAntwerp address
External links
Web of Science
Record
Identifier
Creation 09.01.2024
Last edited 12.02.2024
To cite this reference