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The first chapter, titled "Varieties", deals with the classical algebraic geometry of varieties over algebraically closed fields. This chapter uses many classical results in commutative algebra, including Hilbert's Nullstellensatz, with the books by Atiyah–Macdonald, Matsumura, and Zariski–Samuel as usual references. The second and the ...
The Éléments de géométrie algébrique (EGA; from French: "Elements of Algebraic Geometry") by Alexander Grothendieck (assisted by Jean Dieudonné) is a rigorous treatise on algebraic geometry that was published (in eight parts or fascicles) from 1960 through 1967 by the Institut des Hautes Études Scientifiques.
Foundations of Algebraic Geometry is a book by André Weil (1946, 1962) that develops algebraic geometry over fields of any characteristic. In particular it gives a careful treatment of intersection theory by defining the local intersection multiplicity of two subvarieties .
SGA7 Groupes de monodromie en géométrie algébrique, 1967–1969 (Monodromy groups in algebraic geometry), Lecture Notes in Mathematics 288 and 340, 1972/3. SGA8 was never written. The occasional mentions of SGA8 usually refer to either chapter 8 of SGA1, or Berthelot's work on crystalline cohomology later published outside the SGA series.
It is an important source for his pioneering work on scheme theory, which laid foundations for algebraic geometry in its modern technical developments. The title is a translation of the title of André Weil's book Foundations of Algebraic Geometry. It contained material on descent theory, and existence theorems including that for the Hilbert ...
Igor Rostislavovich Shafarevich (Russian: И́горь Ростисла́вович Шафаре́вич; 3 June 1923 – 19 February 2017) was a Soviet and Russian mathematician who contributed to algebraic number theory and algebraic geometry.
Algebraic geometry is a branch of mathematics which uses abstract algebraic techniques, mainly from commutative algebra, to solve geometrical problems.Classically, it studies zeros of multivariate polynomials; the modern approach generalizes this in a few different aspects.
The terminology of algebraic geometry changed drastically during the twentieth century, with the introduction of the general methods, initiated by David Hilbert and the Italian school of algebraic geometry in the beginning of the century, and later formalized by André Weil, Jean-Pierre Serre and Alexander Grothendieck. Much of the classical ...