ENGLISH

Fundamental algebraic geometry: Grothendieck's FGA explained

By Barbara Fantechi; Lothar Göttsche; Luc Illusie; Steven L. Kleiman; Nitin Nitsure; and Angelo Vistol

Book information

Publisher
American Mathematical Society
Year
2005
ISBN
0821835416, 9780821835418
ISSN
0076-5376
LCC
QA564 .F86 2005
Open Library ID
OL3428915M
Language
english
Format
DJVU
Filesize
3 MB (3019871 bytes)
Series
Mathematical surveys and monographs 123
Pages
352\352
Library
Kolxo3
DPI
600
Scanned
yes
Time added
2009-07-20 03:45:11

Description

Alexander Grothendieck's concepts turned out to be astoundingly powerful and productive, truly revolutionizing algebraic geometry. He sketched his new theories in talks given at the Séminaire Bourbaki between 1957 and 1962. He then collected these lectures in a series of articles in Fondements de la géométrie algébrique (commonly known as FGA). Much of FGA is now common knowledge. However, some of it is less well known, and only a few geometers are familiar with its full scope. The goal of the current book, which resulted from the 2003 Advanced School in Basic Algebraic Geometry (Trieste, Italy), is to fill in the gaps in Grothendieck's very condensed outline of his theories. The four main themes discussed in the book are descent theory, Hilbert and Quot schemes, the formal existence theorem, and the Picard scheme. The authors present complete proofs of the main results, using newer ideas to promote understanding whenever necessary, and drawing connections to later developments. With the main prerequisite being a thorough acquaintance with basic scheme theory, this book is a valuable resource for anyone working in algebraic geometry.

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