000			03260nam a22004215i 4500
001			978-3-8348-9722-0
003			DE-He213
005			20140220084553.0
007			cr nn 008mamaa
008			100805s2010 gw | s |||| 0|eng d
020			_a9783834897220 _9978-3-8348-9722-0
024	7		_a10.1007/978-3-8348-9722-0 _2doi
050		4	_aQA150-272
072		7	_aPBF _2bicssc
072		7	_aMAT002000 _2bisacsh
082	0	4	_a512 _223
100	1		_aGörtz, Ulrich. _eauthor.
245	1	0	_aAlgebraic Geometry I _h[electronic resource] : _bSchemes With Examples and Exercises / _cby Ulrich Görtz, Torsten Wedhorn.
264		1	_aWiesbaden : _bVieweg+Teubner, _c2010.
300			_aIV, 615 p. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
505	0		_aPrevarieties -- 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.
520			_aThis 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
650		0	_aMathematics.
650		0	_aAlgebra.
650	1	4	_aMathematics.
650	2	4	_aAlgebra.
700	1		_aWedhorn, Torsten. _eauthor.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9783834806765
856	4	0	_uhttp://dx.doi.org/10.1007/978-3-8348-9722-0
912			_aZDB-2-SMA
999			_c113029 _d113029