Foundations of Arithmetic Differential Geometry
Alexandru Buium
2017년 6월 · Mathematical Surveys and Monographs 222권 · American Mathematical Soc.
eBook
344
페이지
report검증되지 않은 평점과 리뷰입니다. 자세히 알아보기
eBook 정보
The aim of this book is to introduce and develop an arithmetic analogue of classical differential geometry. In this new geometry the ring of integers plays the role of a ring of functions on an infinite dimensional manifold. The role of coordinate functions on this manifold is played by the prime numbers. The role of partial derivatives of functions with respect to the coordinates is played by the Fermat quotients of integers with respect to the primes. The role of metrics is played by symmetric matrices with integer coefficients. The role of connections (respectively curvature) attached to metrics is played by certain adelic (respectively global) objects attached to the corresponding matrices.
One of the main conclusions of the theory is that the spectrum of the integers is “intrinsically curved”; the study of this curvature is then the main task of the theory. The book follows, and builds upon, a series of recent research papers. A significant part of the material has never been published before.
One of the main conclusions of the theory is that the spectrum of the integers is “intrinsically curved”; the study of this curvature is then the main task of the theory. The book follows, and builds upon, a series of recent research papers. A significant part of the material has never been published before.
저자 정보
Alexandru Buium: University of New Mexico, Albuquerque, NM
이 eBook 평가
의견을 알려주세요.
읽기 정보
스마트폰 및 태블릿
노트북 및 컴퓨터
컴퓨터의 웹브라우저를 사용하여 Google Play에서 구매한 오디오북을 들을 수 있습니다.
eReader 및 기타 기기
Kobo eReader 등의 eBook 리더기에서 읽으려면 파일을 다운로드하여 기기로 전송해야 합니다. 지원되는 eBook 리더기로 파일을 전송하려면 고객센터에서 자세한 안내를 따르세요.
