Fundamental algebraic geometry. Grothendieck'a FGA explained

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 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 Seminaire Bourbaki Between 1957 And 1962. He Then Collected These Lectures In A Series Of Articles In Fondements De La Geometrie Algebrique (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.

Alexander Grothendieck introduced many concepts into algebraic geometry; they turned out to be astoundingly powerful and productive and truly revolutionized the subject. Grothendieck sketched his new theories in a series of talks at the Seminaire Bourbaki between 1957 and 1962 and collected his write-ups in a volume entitled ''Fondements de la Geometrie Algebrique,'' known as FGA. Much of FGA is now common knowledge; however, some of FGA is less well known, and its full scope is familiar to few. The present book resulted from the 2003 ''Advanced School in Basic Algebraic Geometry'' at the ICTP in Trieste, Italy. The book aims to fill in Grothendieck's brief sketches. There are four themes: descent theory, Hilbert and Quot schemes, the formal existence theorem, and the Picard scheme. Most results are proved in full detail; furthermore, newer ideas are introduced to promote understanding, and many connections are drawn to newer developments. The main prerequisite is a thorough acquaintance with basic scheme theory. Thus this book is a valuable resource for anyone doing algebraic geometry.

Alexander Grothendieck introduced many concepts into algebraic geometry; they turned out to be astoundingly powerful and productive and truly revolutionized the subject. Grothendieck sketched his new theories in a series of talks at the Séminaire Bourbaki between 1957 and 1962 and collected his write-ups in a volume entitled “Fondements de la Géométrie Algébrique,” known as FGA. Much of FGA is now common knowledge; however, some of FGA is less well known, and its full scope is familiar to few. The present book resulted from the 2003 “Advanced School in Basic Algebraic Geometry” at the ICTP in Trieste, Italy. The book aims to fill in Grothendieck's brief sketches. There are four themes: descent theory, Hilbert and Quot schemes, the formal existence theorem, and the Picard scheme. Most results are proved in full detail; furthermore, newer ideas are introduced to promote understanding, and many connections are drawn to newer developments. The main prerequisite is a thorough acquaintance with basic scheme theory. Thus this book is a valuable resource for anyone doing algebraic geometry. Resulting from the 2003 Advanced School in Basic Algebraic Geometry (Trieste, Italy), this book aims to fill the gaps in Alexander Grothendieck's condensed outline of his theories. With the main prerequisite being a thorough acquaintance with basic scheme theory, this book is also useful for those working in algebraic geometry. Presents an outline of Alexander Grothendieck's theories. This book discusses four main themes - descent theory, Hilbert and Quot schemes, the formal existence theorem, and the Picard scheme. It is suitable for those working in algebraic geometry.