|
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)
|
|
|
|
|
|
|
Full text (publisher's version - intranet only)
|
|
|
|
|
|