Lectures on An Introduction to Grothendieck's Theory of the Fundamental Group
by J.P. Murre
Publisher: Tata Institute of Fundamental Research 1967
Number of pages: 143
The purpose of this text is to give an introduction to Grothendieck's theory of the fundamental group in algebraic geometry with, as application, the study of the fundamental group of an algebraic curve over an algebraically closed field of arbitrary characteristic.
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by Michael Artin - Tata Institute of Fundamental Research
These notes are based on a series of lectures given in 1973. The lectures are centered about the work of M. Scahlessinger and R. Elkik on infinitesimal deformations. Contents: Formal Theory and Computations; Elkik's Theorems on Algebraization.
by Johan de Jong, et al.
The stacks project aims to build up enough basic algebraic geometry as foundations for algebraic stacks. This implies a good deal of theory on commutative algebra, schemes, varieties, algebraic spaces, has to be developed en route.
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These notes are an introduction to the theory of algebraic varieties. In contrast to most such accounts they study abstract algebraic varieties, not just subvarieties of affine and projective space. This approach leads naturally to scheme theory.
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The monograph gives a detailed exposition of the algorithmic real algebraic geometry. It is well written and will be useful both for beginners and for advanced readers, who work in real algebraic geometry or apply its methods in other fields.