𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Integrality at a prime for global fields and the perfect closure of global fields of characteristic

✍ Scribed by Kirsten Eisenträger

Publisher
Elsevier Science
Year
2005
Tongue
English
Weight
215 KB
Volume
114
Category
Article
ISSN
0022-314X

No coin nor oath required. For personal study only.

✦ Synopsis

Let k be a global field and p any nonarchimedean prime of k. We give a new and uniform proof of the well known fact that the set of all elements of k which are integral at p is diophantine over k. Let k perf be the perfect closure of a global field of characteristic p > 2.

We also prove that the set of all elements of k perf which are integral at some prime q of k perf is diophantine over k perf , and this is the first such result for a field which is not finitely generated over its constant field. This is related to Hilbert's Tenth Problem because for global fields k of positive characteristic, giving a diophantine definition of the set of elements that are integral at a prime is one of two steps needed to prove that Hilbert's Tenth Problem for k is undecidable.

📜 SIMILAR VOLUMES

The prime at infinity and the rank of th
The prime at infinity and the rank of the class group in global function fields
✍ Allison M. Pacelli 📂 Article 📅 2006 🏛 Elsevier Science 🌐 English ⚖ 152 KB

In this paper we construct, for any integers m and n, and 2 g m -1, infinitely many function fields K of degree m over F(T ) such that the prime at infinity splits into exactly g primes in K and the ideal class group of K contains a subgroup isomorphic to (Z/nZ) m-g . This extends previous results o

A Global Solution for the Gravity Field,
A Global Solution for the Gravity Field, Rotation, Landmarks, and Ephemeris of Eros
✍ Alexander S. Konopliv; James K. Miller; William M. Owen; Donald K. Yeomans; Jon 📂 Article 📅 2002 🏛 Elsevier Science 🌐 English ⚖ 814 KB

As part of the NEAR Radio Science investigation, a global solution that includes both spherical and ellipsoidal harmonic gravity fields of Eros, Eros pole and rotation rate, Eros ephemeris, and landmark positions from the optical data was generated. This solution uses the entire one-year in orbit co

Global regularity of the elastic fields
Global regularity of the elastic fields of a power-law model on Lipschitz domains
✍ Dorothee Knees 📂 Article 📅 2006 🏛 John Wiley and Sons 🌐 English ⚖ 262 KB

Understanding the interaction between various processes is a pre-requisite for solving problems in natural and engineering sciences. Many phenomena can not be described by concentrating on them in isolation - therefore multifield models and concepts that include various kinds of field problems and p