TY  - GEN
AU  - Fantechi,Barbara
AU  - Göttsche,Lothar
AU  - Illusie,Luc
AU  - Kleiman,Steven L.
AU  - Nitsure,Nitin
AU  - Vistoli,Angelo
TI  - Fundamental algebraic geometry: Grothendieck's FGA explained
T2  - Mathematical surveys and monographs,
SN  - 0821842455
U1  - 514.7 
PY  - 2005///
CY  - Providence, R.I.
PB  - American Mathematical Society
KW  - Geometry, Algebraic
KW  - Grothendieck groups
KW  - Grothendieck categories
N1  - Includes bibliographical references (p. 323-331) and index; Readership: Graduate students and research mathematicians interested in algebraic geometry
N2  - 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
UR  - https://www.ams.org/books/surv/123/surv123-endmatter.pdf
UR  - https://www.goodreads.com/book/show/2170336.Fundamental_Algebraic_Geometry?ref=nav_sb_ss_1_13#CommunityReviews
ER  -