Algebraic Geometry and Commutative Algebra (Universitext)
De (autor) Siegfried Boschen Limba Engleză Carte Paperback – 16 Nov 2012
The scheme-theoretic approach to algebraic geometry is explained for non-experts. More advanced readers can use the book to broaden their view on the subject. A separate part deals with the necessary prerequisites from commutative algebra. On a whole, the book provides a very accessible and self-contained introduction to algebraic geometry, up to a quite advanced level.
Every chapter of the book is preceded by a motivating introduction with an informal discussion of the contents. Typical examples and an abundance of exercises illustrate each section. This way the book is an excellent solution for learning by yourself or for complementing knowledge that is already present. It can equally be used as a convenient source for courses and seminars or as supplemental literature.
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Specificații
ISBN-13: 9781447148289
ISBN-10: 1447148282
Pagini: 516
Ilustrații: 1
Dimensiuni: 155 x 235 x 27 mm
Greutate: 0.71 kg
Ediția: 2013
Editura: SPRINGER LONDON
Colecția Springer
Seria Universitext
Locul publicării: London, United Kingdom
ISBN-10: 1447148282
Pagini: 516
Ilustrații: 1
Dimensiuni: 155 x 235 x 27 mm
Greutate: 0.71 kg
Ediția: 2013
Editura: SPRINGER LONDON
Colecția Springer
Seria Universitext
Locul publicării: London, United Kingdom
Public țintă
GraduateCuprins
Rings
and
Modules.-
The
Theory
of
Noetherian
Rings.-
Integral
Extensions.-
Extension
of
Coefficients
and
Descent.-
Homological
Methods:
Ext
and
Tor.-
Affine
Schemes
and
Basic
Constructions.-
Techniques
of
Global
Schemes.-
Etale
and
Smooth
Morphisms.-
Projective
Schemes
and
Proper
Morphisms.
Recenzii
From
the
reviews:
“The book under review is a self-contained introduction to both fields and their relationship and is divided into two parts. … The book is well written and there are exercises at the end of the chapter sections. … this is certainly a welcome addition to the library of anyone interested in these fields.” (Cícero Carvalho, Mathematical Reviews, September, 2013)
“Bosch (Wilhelms Univ., Westphalia, Germany) offers an introduction to scheme-theoretic algebraic geometry preceded by an extended treatment of the prerequisite commutative algebra. … this is a useful, self-contained work for those interested in studying the modern approach to the subject. Summing Up: Recommended. Graduate students and researchers/faculty.” (S. J. Colley, Choice, Vol. 50 (10), June, 2013)
“The book is carefully written, with good examples, detailed proofs, and plenty of exercises at the end of every one of its sections. Each chapter has an introduction where the author discusses informally and motivates the contents of the chapter. I liked the book and I believe that it can be used either as textbook for a two-semester introduction to algebraic geometry or for self-study by a motivated student.” (Felipe Zaldivar, MAA Reviews, March, 2013)
“Book under review is to introduce the basic concepts and methods of modern algebraic geometry to novices in the field … . each chapter comes with its own introduction, where the author motivates the respective contents by illustrating examples and spotlights the main aspects. … a useful glossary of notations, a comprehensive index, and a list of hints for further reading facilitate working with this textbook considerably. … the current book is an excellent primer on the elements of modern algebraic geometry and commutative algebra.” (Werner Kleinert, Zentralblatt MATH, Vol. 1257, 2013)
“The book under review is a self-contained introduction to both fields and their relationship and is divided into two parts. … The book is well written and there are exercises at the end of the chapter sections. … this is certainly a welcome addition to the library of anyone interested in these fields.” (Cícero Carvalho, Mathematical Reviews, September, 2013)
“Bosch (Wilhelms Univ., Westphalia, Germany) offers an introduction to scheme-theoretic algebraic geometry preceded by an extended treatment of the prerequisite commutative algebra. … this is a useful, self-contained work for those interested in studying the modern approach to the subject. Summing Up: Recommended. Graduate students and researchers/faculty.” (S. J. Colley, Choice, Vol. 50 (10), June, 2013)
“The book is carefully written, with good examples, detailed proofs, and plenty of exercises at the end of every one of its sections. Each chapter has an introduction where the author discusses informally and motivates the contents of the chapter. I liked the book and I believe that it can be used either as textbook for a two-semester introduction to algebraic geometry or for self-study by a motivated student.” (Felipe Zaldivar, MAA Reviews, March, 2013)
“Book under review is to introduce the basic concepts and methods of modern algebraic geometry to novices in the field … . each chapter comes with its own introduction, where the author motivates the respective contents by illustrating examples and spotlights the main aspects. … a useful glossary of notations, a comprehensive index, and a list of hints for further reading facilitate working with this textbook considerably. … the current book is an excellent primer on the elements of modern algebraic geometry and commutative algebra.” (Werner Kleinert, Zentralblatt MATH, Vol. 1257, 2013)
Textul de pe ultima copertă
Algebraic
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.
Moreover,
Grothendieck’s
schemes
invented
in
the
late
1950s
allowed
the
application
of
algebraic-geometric
methods
in
fields
that
formerly
seemed
to
be
far
away
from
geometry
(algebraic
number
theory,
for
example).
The
new
techniques
paved
the
way
to
spectacular
progress
such
as
the
proof
of
Fermat’s
Last
Theorem
by
Wiles
and
Taylor.
The scheme-theoretic approach to algebraic geometry is explained for non-experts whilst more advanced readers can use the book to broaden their view on the subject. A separate part studies the necessary prerequisites from commutative algebra. The book provides an accessible and self-contained introduction to algebraic geometry, up to an advanced level.
Every chapter of the book is preceded by a motivating introduction with an informal discussion of the contents. Typical examples and an abundance of exercises illustrate each section. Therefore the book is an excellent solution for learning by yourself or for complementing knowledge that is already present. It can equally be used as a convenient source for courses and seminars or as supplemental literature.
The scheme-theoretic approach to algebraic geometry is explained for non-experts whilst more advanced readers can use the book to broaden their view on the subject. A separate part studies the necessary prerequisites from commutative algebra. The book provides an accessible and self-contained introduction to algebraic geometry, up to an advanced level.
Every chapter of the book is preceded by a motivating introduction with an informal discussion of the contents. Typical examples and an abundance of exercises illustrate each section. Therefore the book is an excellent solution for learning by yourself or for complementing knowledge that is already present. It can equally be used as a convenient source for courses and seminars or as supplemental literature.
Caracteristici
Explains
schemes
in
algebraic
geometry
from
a
beginner's
level
up
to
advanced
topics
such
as
smoothness
and
ample
invertible
sheaves
Is self-contained and well adapted for self-study
Includes prerequisites from commutative algebra in a separate part
Gives motivating introductions to the different themes, illustrated by typical examples
Offers an abundance of exercises, specially adapted to the different sections
Is self-contained and well adapted for self-study
Includes prerequisites from commutative algebra in a separate part
Gives motivating introductions to the different themes, illustrated by typical examples
Offers an abundance of exercises, specially adapted to the different sections