Algebraic Geometry
Part I: Schemes. With Examples and Exercises
Görtz, Ulrich.
creator
author.
aut
http://id.loc.gov/vocabulary/relators/aut
Wedhorn, Torsten.
author.
aut
http://id.loc.gov/vocabulary/relators/aut
SpringerLink (Online service)
text
gw
2010
1st ed. 2010.
monographic
eng
access
IV, 615 p. online resource.
This book introduces the reader to modern algebraic geometry. It presents Grothendieck's technically demanding language of schemes that is the basis of the most important developments in the last fifty years within this area. A systematic treatment and motivation of the theory is emphasized, using concrete examples to illustrate its usefulness. Several examples from the realm of Hilbert modular surfaces and of determinantal varieties are used methodically to discuss the covered techniques. Thus the reader experiences that the further development of the theory yields an ever better understanding of these fascinating objects. The text is complemented by many exercises that serve to check the comprehension of the text, treat further examples, or give an outlook on further results. The volume at hand is an introduction to schemes. To get startet, it requires only basic knowledge in abstract algebra and topology. Essential facts from commutative algebra are assembled in an appendix. It will be complemented by a second volume on the cohomology of schemes. Prevarieties - Spectrum of a Ring - Schemes - Fiber products - Schemes over fields - Local properties of schemes - Quasi-coherent modules - Representable functors - Separated morphisms - Finiteness Conditions - Vector bundles - Affine and proper morphisms - Projective morphisms - Flat morphisms and dimension - One-dimensional schemes - Examples Prof. Dr. Ulrich Görtz, Institute of Experimental Mathematics, University Duisburg-Essen Prof. Dr. Torsten Wedhorn, Department of Mathematics, University of Paderborn.
Prevarieties -- Spectrum of a Ring -- Schemes -- Fiber products -- Schemes over fields -- Local Properties of Schemes -- Quasi-coherent modules -- Representable Functors -- Separated morphisms -- Finiteness Conditions -- Vector bundles -- Affine and proper morphisms -- Projective morphisms -- Flat morphisms and dimension -- One-dimensional schemes -- Examples.
by Ulrich Görtz, Torsten Wedhorn.
Algebraic geometry
Algebra
Algebraic Geometry
Algebra
QA564-609
516.35
Springer Nature eBook
Advanced Lectures in Mathematics
9783834897220
https://doi.org/10.1007/978-3-8348-9722-0
https://doi.org/10.1007/978-3-8348-9722-0
100805
20210921163821.0
978-3-8348-9722-0