000			02201nam a2200277Ia 4500
003			OSt
005			20240129160312.0
008			231229s9999 xx 000 0 und d
020			_a9781447175223
040			_cIISER BPR
041			_aEng
082			_a516.35 _bBOS _223rd
100			_aBosch, Siefried
245		0	_aAlgebraic geometry and communicative algebra
250			_a2nd ed.
260			_aLondon: _bSpringer-Verlag, _cc2022.
300			_ax, 504p. : _bill. ; _c22cm.
520			_aAlgebraic Geometry is a fascinating branch of Mathematics that combines methods from both Algebra and Geometry. It transcends the limited scope of pure Algebra by means of geometric construction principles. Putting forward this idea, Grothendieck revolutionized Algebraic Geometry in the late 1950s by inventing schemes. Schemes now also play an important role in Algebraic Number Theory, a field that used to be far away from Geometry. The new point of view paved the way for spectacular progress, such as the proof of Fermat's Last Theorem by Wiles and Taylor. This book explains the scheme-theoretic approach to Algebraic Geometry for non-experts, while more advanced readers can use it to broaden their view on the subject. A separate part presents the necessary prerequisites from Commutative Algebra, thereby providing an accessible and self-contained introduction to advanced Algebraic Geometry. Every chapter of the book is preceded by a motivating introduction with an informal discussion of its contents and background. Typical examples, and an abundance of exercises illustrate each section. Therefore the book is an excellent companion for self-studying or for complementing skills that have already been acquired. It can just as well serve as a convenient source for (reading) course material and, in any case, as supplementary literature. The present edition is a critical revision of the earlier text. Also includes bibliographic references, glossary of notations and index.
650			_aMathematics
650			_aCommutative algebra
650			_aAlgebraic geometry
650			_aProjective schemes
942			_cBK _2ddc
947			_a5702.8724999999995
948			_a22
999			_c3255 _d3255