000			02374nam a22003017a 4500
003			OSt
005			20240615181328.0
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020			_a9783658430306
040			_aNISER LIBRARY _beng _cNISER LIBRARY
041			_aEnglish
082	0	0	_a512.7 _bGOR-A
100	1		_aGörtz, Ulrich.
245	1	0	_aAlgebraic geometry II : _bcohomology of schemes: with examples and exercises
260			_aGermany : _bSpringer Spektrum, _c2023.
300			_avii, 869p.
490			_aSpringer studium mathematik - master _x2509-9310
520			_aThis book completes the comprehensive introduction to modern algebraic geometry which was started with the introductory volume Algebraic Geometry I: Schemes. It begins by discussing in detail the notions of smooth, unramified and étale morphisms including the étale fundamental group. The main part is dedicated to the cohomology of quasi-coherent sheaves. The treatment is based on the formalism of derived categories which allows an efficient and conceptual treatment of the theory, which is of crucial importance in all areas of algebraic geometry. After the foundations are set up, several more advanced topics are studied, such as numerical intersection theory, an abstract version of the Theorem of Grothendieck-Riemann-Roch, the Theorem on Formal Functions, Grothendieck's algebraization results and a very general version of Grothendieck duality. The book concludes with chapters on curves and on abelian schemes, which serve to develop the basics of the theory of these two important classes of schemes on an advanced level, and at the same time to illustrate the power of the techniques introduced previously. The text contains many exercises that allow the reader to check their comprehension of the text, present further examples or give an outlook on further results.
650			_aAlgebraic Geometry.
650			_aGeometry, Algebraic.
650			_aCohomology of Schemes
650			_aSmooth Morphisms
650			_aCohomology of Sheaves of Modules
700	1		_aWedhorn, Torsten.
856			_3Table of contents _uhttps://link.springer.com/content/pdf/bfm:978-3-658-43031-3/1
856			_3Reviews _uhttps://www.goodreads.com/book/show/211896624-algebraic-geometry-ii?from_search=true&from_srp=true&qid=XxtAKoWWjS&rank=2#CommunityReviews
942			_cBK _2udc
999			_c35047 _d35047