Abhyankar, Shreeram Shankar
Overview
Works:  53 works in 270 publications in 4 languages and 7,102 library holdings 

Genres:  Conference proceedings Textbooks 
Roles:  Author, Honoree, Editor 
Classifications:  QA3, 516.35 
Publication Timeline
.
Most widely held works by
Shreeram Shankar Abhyankar
Local analytic geometry
by
Shreeram Shankar Abhyankar(
)
31 editions published between 1964 and 2001 in 3 languages and held by 1,790 WorldCat member libraries worldwide
This book provides, for use in a graduate course or for selfstudy by graduate students, a wellmotivated treatment of several topics, especially the following: algebraic treatment of several complex variables; geometric approach to algebraic geometry via analytic sets; survey of local algebra; and survey of sheaf theory. The book has been written in the spirit of Weierstrass. Power series play the dominant role. The treatment, being algebraic, is not restricted to complex numbers, but remains valid over any completevalued field. This makes it applicable to situations arising from number theory. When it is specialized to the complex case, connectivity and other topological properties come to the fore. In particular, via singularities of analytic sets, topological fundamental groups can be studied. In the transition from punctual to local, ie. from properties at a point to properties near a point, the classical work of Osgood plays an important role. This gives rise to normic forms and the concept of the Osgoodian. Following Serre, the passage from local to global properties of analytic spaces is facilitated by introducing sheaf theory. Here the fundamental results are the coherence theorems of Oka and Cartan. They are followed by theory normalization due to Oka and Zariski in the analytic and algebraic cases, respectively
31 editions published between 1964 and 2001 in 3 languages and held by 1,790 WorldCat member libraries worldwide
This book provides, for use in a graduate course or for selfstudy by graduate students, a wellmotivated treatment of several topics, especially the following: algebraic treatment of several complex variables; geometric approach to algebraic geometry via analytic sets; survey of local algebra; and survey of sheaf theory. The book has been written in the spirit of Weierstrass. Power series play the dominant role. The treatment, being algebraic, is not restricted to complex numbers, but remains valid over any completevalued field. This makes it applicable to situations arising from number theory. When it is specialized to the complex case, connectivity and other topological properties come to the fore. In particular, via singularities of analytic sets, topological fundamental groups can be studied. In the transition from punctual to local, ie. from properties at a point to properties near a point, the classical work of Osgood plays an important role. This gives rise to normic forms and the concept of the Osgoodian. Following Serre, the passage from local to global properties of analytic spaces is facilitated by introducing sheaf theory. Here the fundamental results are the coherence theorems of Oka and Cartan. They are followed by theory normalization due to Oka and Zariski in the analytic and algebraic cases, respectively
Resolution of singularities of embedded algebraic surfaces
by
Shreeram Shankar Abhyankar(
Book
)
24 editions published between 1966 and 2011 in English and Italian and held by 856 WorldCat member libraries worldwide
This new edition describes the geometric part of the author's 1965 proof of desingularization of algebraic surfaces and solids in nonzero characteristic. The book also provides a selfcontained introduction to birational algebraic geometry, based only on basic commutative algebra. In addition, it gives a short proof of analytic desingularization in characteristic zero for any dimension found in 1996 and based on a new avatar of an algorithmic trick employed in the original edition of the book. This new edition will inspire further progress in resolution of singularities of algebraic and arithmetical varieties which will be valuable for applications to algebraic geometry and number theory. It can can be used for a second year graduate course. The reference list has been updated
24 editions published between 1966 and 2011 in English and Italian and held by 856 WorldCat member libraries worldwide
This new edition describes the geometric part of the author's 1965 proof of desingularization of algebraic surfaces and solids in nonzero characteristic. The book also provides a selfcontained introduction to birational algebraic geometry, based only on basic commutative algebra. In addition, it gives a short proof of analytic desingularization in characteristic zero for any dimension found in 1996 and based on a new avatar of an algorithmic trick employed in the original edition of the book. This new edition will inspire further progress in resolution of singularities of algebraic and arithmetical varieties which will be valuable for applications to algebraic geometry and number theory. It can can be used for a second year graduate course. The reference list has been updated
Geometric theory of algebraic space curves
by
Shreeram Shankar Abhyankar(
Book
)
17 editions published in 1974 in English and German and held by 550 WorldCat member libraries worldwide
17 editions published in 1974 in English and German and held by 550 WorldCat member libraries worldwide
Lectures on algebra
by
Shreeram Shankar Abhyankar(
)
14 editions published in 2006 in English and held by 527 WorldCat member libraries worldwide
14 editions published in 2006 in English and held by 527 WorldCat member libraries worldwide
Algebraic geometry for scientists and engineers
by
Shreeram Shankar Abhyankar(
Book
)
14 editions published between 1990 and 2000 in English and held by 525 WorldCat member libraries worldwide
14 editions published between 1990 and 2000 in English and held by 525 WorldCat member libraries worldwide
Weighted expansions for canonical desingularization
by
Shreeram Shankar Abhyankar(
Book
)
17 editions published between 1982 and 2008 in 3 languages and held by 497 WorldCat member libraries worldwide
17 editions published between 1982 and 2008 in 3 languages and held by 497 WorldCat member libraries worldwide
Ramification theoretic methods in algebraic geometry
by
Shreeram Shankar Abhyankar(
Book
)
22 editions published between 1956 and 1994 in 3 languages and held by 484 WorldCat member libraries worldwide
22 editions published between 1956 and 1994 in 3 languages and held by 484 WorldCat member libraries worldwide
Algebraic geometry; papers presented at the Bombay Colloquium, 1968
by International Colloquium on Algebraic Geometry(
Book
)
15 editions published between 1968 and 1969 in English and Undetermined and held by 306 WorldCat member libraries worldwide
15 editions published between 1968 and 1969 in English and Undetermined and held by 306 WorldCat member libraries worldwide
Enumerative combinatorics of Young tableaux
by
Shreeram Shankar Abhyankar(
Book
)
8 editions published in 1988 in English and Undetermined and held by 277 WorldCat member libraries worldwide
8 editions published in 1988 in English and Undetermined and held by 277 WorldCat member libraries worldwide
Algebraic space curves
by
Shreeram Shankar Abhyankar(
Book
)
13 editions published in 1971 in 3 languages and held by 270 WorldCat member libraries worldwide
13 editions published in 1971 in 3 languages and held by 270 WorldCat member libraries worldwide
Recent developments in the inverse Galois problem : a Joint Summer Research Conference on Recent Developments in the Inverse Galois Problem, July 1723, 1993, University of Washington, Seattle
by Joint Summer Research Conference on Recent Developments in the Inverse Galois Problem(
Book
)
4 editions published in 1995 in English and held by 232 WorldCat member libraries worldwide
Group theory and a first course in algebraic curves are sufficient for understanding many papers in the volume. Graduate students will find this an excellent reference to current research, as it contains a list of problems appropriate for thesis material in arithmetic geometry, algebraic number theory, and group theory
4 editions published in 1995 in English and held by 232 WorldCat member libraries worldwide
Group theory and a first course in algebraic curves are sufficient for understanding many papers in the volume. Graduate students will find this an excellent reference to current research, as it contains a list of problems appropriate for thesis material in arithmetic geometry, algebraic number theory, and group theory
Algebraic geometry and its applications : collections of papers from Shreeram S. Abhyankar's 60th birthday conference
by
Chandrajit Bajaj(
Book
)
9 editions published in 1994 in English and held by 215 WorldCat member libraries worldwide
Algebraic Geometry and its Applications will be of interest not only to mathematicians but also to computer scientists working on visualization and related topics. The book is based on 32 invited papers presented at a conference in honor of Shreeram Abhyankar's 60th birthday, which was held in June 1990 at Purdue University and attended by many renowned mathematicians (field medalists), computer scientists and engineers. The keynote paper is by G. Birkhoff; other contributors include such leading names in algebraic geometry as R. Hartshorne, J. Heintz, J.I. Igusa, D. Lazard, D. Mumford, and J.P. Serre
9 editions published in 1994 in English and held by 215 WorldCat member libraries worldwide
Algebraic Geometry and its Applications will be of interest not only to mathematicians but also to computer scientists working on visualization and related topics. The book is based on 32 invited papers presented at a conference in honor of Shreeram Abhyankar's 60th birthday, which was held in June 1990 at Purdue University and attended by many renowned mathematicians (field medalists), computer scientists and engineers. The keynote paper is by G. Birkhoff; other contributors include such leading names in algebraic geometry as R. Hartshorne, J. Heintz, J.I. Igusa, D. Lazard, D. Mumford, and J.P. Serre
Algebra, arithmetic and geometry with applications : papers from Shreeram S. Abhyankar's 70th birthday conference
by
C Christensen(
Book
)
5 editions published between 2003 and 2004 in English and held by 122 WorldCat member libraries worldwide
This volume is the proceedings of the Conference on Algebra and Algebraic Geometry with Applications which was held July 19 26, 2000, at Purdue University to honor Professor Shreeram S. Abhyankar on the occasion of his seventieth birthday. Eightyfive of Professor Abhyankar's students, collaborators, and colleagues were invited participants. Sixty participants presented papers related to Professor Abhyankar's broad areas of mathematical interest. There were sessions on algebraic geometry, singularities, group theory, Galois theory, combinatorics, Drinfield modules, affine geometry, and the Jacobian problem. This volume offers an outstanding collection of papers by authors who are among the experts in their areas
5 editions published between 2003 and 2004 in English and held by 122 WorldCat member libraries worldwide
This volume is the proceedings of the Conference on Algebra and Algebraic Geometry with Applications which was held July 19 26, 2000, at Purdue University to honor Professor Shreeram S. Abhyankar on the occasion of his seventieth birthday. Eightyfive of Professor Abhyankar's students, collaborators, and colleagues were invited participants. Sixty participants presented papers related to Professor Abhyankar's broad areas of mathematical interest. There were sessions on algebraic geometry, singularities, group theory, Galois theory, combinatorics, Drinfield modules, affine geometry, and the Jacobian problem. This volume offers an outstanding collection of papers by authors who are among the experts in their areas
Lectures on algebra
by
Shreeram Shankar Abhyankar(
Book
)
6 editions published in 2006 in English and held by 109 WorldCat member libraries worldwide
6 editions published in 2006 in English and held by 109 WorldCat member libraries worldwide
Geometry and analysis : papers presented at the Bombay colloquium 1992
(
Book
)
7 editions published in 1995 in English and French and held by 102 WorldCat member libraries worldwide
7 editions published in 1995 in English and French and held by 102 WorldCat member libraries worldwide
Lectures on expansion techniques in algebraic geometry
by
Shreeram Shankar Abhyankar(
Book
)
8 editions published in 1977 in English and Undetermined and held by 96 WorldCat member libraries worldwide
8 editions published in 1977 in English and Undetermined and held by 96 WorldCat member libraries worldwide
Algebraic surfaces
by
Oscar Zariski(
Book
)
7 editions published in 1971 in 3 languages and held by 41 WorldCat member libraries worldwide
7 editions published in 1971 in 3 languages and held by 41 WorldCat member libraries worldwide
Encyclopaedia of Mathematics, Supplement III
by
Shreeram Shankar Abhyankar(
)
2 editions published in 2002 in English and held by 19 WorldCat member libraries worldwide
This is the third supplementary volume to Kluwer's highly acclaimed twelvevolume Encyclopaedia of Mathematics. This additional volume contains nearly 500 new entries written by experts and covers developments and topics not included in the previous volumes. These entries are arranged alphabetically throughout and a detailed index is included. This supplementary volume enhances the existing twelve volumes, and together, these thirteen volumes represent the most authoritative, comprehensive and uptodate Encyclopaedia of Mathematics available
2 editions published in 2002 in English and held by 19 WorldCat member libraries worldwide
This is the third supplementary volume to Kluwer's highly acclaimed twelvevolume Encyclopaedia of Mathematics. This additional volume contains nearly 500 new entries written by experts and covers developments and topics not included in the previous volumes. These entries are arranged alphabetically throughout and a detailed index is included. This supplementary volume enhances the existing twelve volumes, and together, these thirteen volumes represent the most authoritative, comprehensive and uptodate Encyclopaedia of Mathematics available
Lectures on Algebra  Volume 1
by
Shreeram Shankar Abhyankar(
)
2 editions published in 2006 in English and held by 11 WorldCat member libraries worldwide
This book is a timely survey of much of the algebra developed during the last several centuries including its applications to algebraic geometry and its potential use in geometric modeling. The present volume makes an ideal textbook for an abstract algebra course, while the forthcoming sequel, Lectures on Algebra II, will serve as a textbook for a linear algebra course. The author's fondness for algebraic geometry shows up in both volumes, and his recent preoccupation with the applications of group theory to the calculation of Galois groups is evident in the second volume which contains more lo
2 editions published in 2006 in English and held by 11 WorldCat member libraries worldwide
This book is a timely survey of much of the algebra developed during the last several centuries including its applications to algebraic geometry and its potential use in geometric modeling. The present volume makes an ideal textbook for an abstract algebra course, while the forthcoming sequel, Lectures on Algebra II, will serve as a textbook for a linear algebra course. The author's fondness for algebraic geometry shows up in both volumes, and his recent preoccupation with the applications of group theory to the calculation of Galois groups is evident in the second volume which contains more lo
Bombay rents control act : Bombay act no. 57 of 1947 : as amended up to date, with full commentary, rules & notifications
by
Bombay (India : State)(
Book
)
1 edition published in 1964 in English and held by 8 WorldCat member libraries worldwide
1 edition published in 1964 in English and held by 8 WorldCat member libraries worldwide
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Related Identities
 Sathaye, A. M. (Avinash Madhav) 1948 Editor
 International Mathematical Union
 Fried, Michael D. 1942 Editor
 American Mathematical Society
 Bajaj, Chanderjit 1958 Editor
 Christensen, C. (Chris) 1946 Editor
 Sundaram, G. (Ganesh) 1965 Editor
 Tata Institute of Fundamental Research
 SpringerLink (Service en ligne)
 Zariski, Oscar Author
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Associated Subjects
Algebra Algebra, Abstract Algebraic fields Algebraic varieties Algebras, Linear Arithmetic Canada College teachers Combinatorial enumeration problems Curves, Algebraic Functional analysis Geometry Geometry, Algebraic Geometry, Analytic Geometry, Differential Global analysis (Mathematics) IndiaBombay (State) Inverse Galois theory Jacobians Mappings (Mathematics) Mathematical analysis Mathematics Number theory Rent control Research Rings (Algebra) Scientists Singularities (Mathematics) Surfaces Surfaces, Algebraic United States Young tableaux
Alternative Names
Abhyankar, S.
Abhyankar, S. S.
Abhyankar, S. S. 1930
Abhyankar, S. S. (Shreeram Shankar)
Abhyankar, Shreeram 1930
Abhyankar, Shreeram S.
Abhyankar, Shreeram S. 1930
Abhyankar, Shreeram S. (Shreeram Shankar)
Abhyankar, Shreeram Shankar 1930
Shankar Abhyankar, Shreeram 1930
Shreeram Shankar Abhyankar
Shreeram Shankar Abhyankar 1930....
Shreeram Shankar Abhyanker.
Shreeram Shankar Abhyanker 1930
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