The study of arithmetic differential operators is a novel and promising area of mathematics. This complete introduction to the subject starts with the basics: a discussion of p-adic numbers and some of the classical differential analysis on the field of p-adic numbers leading to the definition of arithmetic differential operators on this field. Buium's theory of arithmetic jet spaces is then developed succinctly in order to define arithmetic operators in general. Features of the book include a comparison of the behaviour of these operators over the p-adic integers and their behaviour over the unramified completion, and a discussion of the relationship between characteristic functions of p-adic discs and arithmetic differential operators that disappears as soon as a single root of unity is adjoined to the p-adic integers. This book is essential reading for researchers and graduate students who want a first introduction to arithmetic differential operators over the p-adic integers.
| ISBN: | 9781107674141 |
| Publication date: | 26th January 2012 |
| Author: | Claire C Ralph, S R Simanca, London Mathematical Society |
| Publisher: | Cambridge University Press |
| Format: | Paperback |
| Pagination: | 139 pages |
| Series: | London Mathematical Society Lecture Note Series |
| Genres: |
Algebraic geometry |
The study of arithmetic differential operators is a novel and promising area of mathematics. This complete introduction to the subject starts with the basics: a discussion of p-adic numbers and some of the classical differential analysis on the field of p-adic numbers leading to the definition of arithmetic differential operators on this field. Buium's theory of arithmetic jet spaces is then developed succinctly in order to define arithmetic operators in general. Features of the book include a comparison of the behaviour of these operators over the p-adic integers and their behaviour over the unramified completion, and a discussion of the relationship between characteristic functions of p-adic discs and arithmetic differential operators that disappears as soon as a single root of unity is adjoined to the p-adic integers. This book is essential reading for researchers and graduate students who want a first introduction to arithmetic differential operators over the p-adic integers.
Arithmetic Differential Operators Over the P-Adic Integers features in the following genres: Algebraic geometry
Arithmetic Differential Operators Over the P-Adic Integers is available in Paperback
Arithmetic Differential Operators Over the P-Adic Integers was written by Claire C Ralph, S R Simanca, London Mathematical Society and published by Cambridge University Press
Arithmetic Differential Operators Over the P-Adic Integers has 139 pages
Yes it is part of London Mathematical Society Lecture Note Series series
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