Lectures on Forms in Many Variables - Softcover

Greenberg, Marvin J

Softcover

ISBN 10: 4871877302 ISBN 13: 9784871877305

Publisher: Ishi Press, 2018

Synopsis

This book, based on lectures delivered at the University of California, Santa Cruz in 1968, surveys the many different co-efficient fields for which a homogeneous polynomial in many variables has a non-trivial zero. The book gives a complete treatment of the elementary part of this theorem and includes discussions, without complete proofs, of the more advanced results, giving appropriate references and indications of relations with other subjects, such as class field theory, algebraic geometry and analytic number theory, Problems for further research are also presented. The book is designed for use as the main text in a senior or graduate level course. The level of the discussions required familiarity with material covered in an undergraduate course in rings and fields.

About this title

About the Author

Marvin Jay Greenberg was Emeritus Professor of Mathematics, University of California at Santa Cruz. He was born on 22 December 1935. He received his undergraduate degree from Columbia University, where he was a Ford Scholar. His PhD is from Princeton University, his thesis adviser having been the brilliant and fiery Serge Lang. He was subsequently an Assistant Professor at U.C. Berkeley for five years (two years of which he spent on NSF Postdoctoral Fellowships at Harvard and at the I.H.E.S. in Paris), an Associate Professor at Northeastern University for two years, and Full Professor at U.C. Santa Cruz for twenty five years. He took early retirement from that campus at age 57. His first published book was Lectures on Algebraic Topology in 1967, which was later expanded into a joint work with John Harper, Algebraic Topology: A First Course (Westview, 1981). His second book Lectures on Forms in Many Variables (1969) was about the subject started by Serge Lang in his thesis and subsequently developed by himself and others, culminating in the great theorem of Ax and Kochen showing that the conjecture of Emil Artin that p-adic fields are C2 is "almost true" (Terjanian found the first counter-example to the full conjecture). His Freeman text Euclidean and Non-Euclidean Geometries: Development and History had its first edition appear in 1974, and is now in its vastly expanded fourth edition. His early journal publications are in the subject of algebraic geometry, where he discovered a functor J.-P. Serre named after him and an approximation theorem J. Nicaise and J. Sebag named after him. Professor Greenberg lived alone in Berkeley, CA, and had an adult son who lives on the boat his son owns. Marvin died suddenly in Berkeley on December 12, 2017.

Edition details

• Publisher: Ishi Press
• Publication date: 2018
• Language: English
• ISBN 10: 4871877302
• ISBN 13: 9784871877305
• Binding: Paperback
• Number of pages: 184