Arithmetic Algebraic Geometry - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Arithmetic Algebraic Geometry write by Brian David Conrad. This book was released on . Arithmetic Algebraic Geometry available in PDF, EPUB and Kindle. The articles in this volume are expanded versions of lectures delivered at the Graduate Summer School and at the Mentoring Program for Women in Mathematics held at the Institute for Advanced Study/Park City Mathematics Institute. The theme of the program was arithmetic algebraic geometry. The choice of lecture topics was heavily influenced by the recent spectacular work of Wiles on modular elliptic curves and Fermat's Last Theorem. The main emphasis of the articles in the volume is on elliptic curves, Galois representations, and modular forms. One lecture series offers an introduction to these objects. The others discuss selected recent results, current research, and open problems and conjectures. The book would be a suitable text for an advanced graduate topics course in arithmetic algebraic geometry.
Algebra, Arithmetic, and Geometry
Algebra, Arithmetic, and Geometry - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Algebra, Arithmetic, and Geometry write by Yuri Tschinkel. This book was released on 2010-04-11. Algebra, Arithmetic, and Geometry available in PDF, EPUB and Kindle. EMAlgebra, Arithmetic, and Geometry: In Honor of Yu. I. ManinEM consists of invited expository and research articles on new developments arising from Manin’s outstanding contributions to mathematics.
Algebraic Geometry and Arithmetic Curves
Algebraic Geometry and Arithmetic Curves - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Algebraic Geometry and Arithmetic Curves write by Qing Liu. This book was released on 2006-06-29. Algebraic Geometry and Arithmetic Curves available in PDF, EPUB and Kindle. This book is a general introduction to the theory of schemes, followed by applications to arithmetic surfaces and to the theory of reduction of algebraic curves. The first part introduces basic objects such as schemes, morphisms, base change, local properties (normality, regularity, Zariski's Main Theorem). This is followed by the more global aspect: coherent sheaves and a finiteness theorem for their cohomology groups. Then follows a chapter on sheaves of differentials, dualizing sheaves, and Grothendieck's duality theory. The first part ends with the theorem of Riemann-Roch and its application to the study of smooth projective curves over a field. Singular curves are treated through a detailed study of the Picard group. The second part starts with blowing-ups and desingularisation (embedded or not) of fibered surfaces over a Dedekind ring that leads on to intersection theory on arithmetic surfaces. Castelnuovo's criterion is proved and also the existence of the minimal regular model. This leads to the study of reduction of algebraic curves. The case of elliptic curves is studied in detail. The book concludes with the funadmental theorem of stable reduction of Deligne-Mumford. The book is essentially self-contained, including the necessary material on commutative algebra. The prerequisites are therefore few, and the book should suit a graduate student. It contains many examples and nearly 600 exercises.
Algebra & Geometry
Algebra & Geometry - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Algebra & Geometry write by Mark V. Lawson. This book was released on 2016-11-25. Algebra & Geometry available in PDF, EPUB and Kindle. Algebra & Geometry: An Introduction to University Mathematics provides a bridge between high school and undergraduate mathematics courses on algebra and geometry. The author shows students how mathematics is more than a collection of methods by presenting important ideas and their historical origins throughout the text. He incorporates a hands-on approach to proofs and connects algebra and geometry to various applications. The text focuses on linear equations, polynomial equations, and quadratic forms. The first several chapters cover foundational topics, including the importance of proofs and properties commonly encountered when studying algebra. The remaining chapters form the mathematical core of the book. These chapters explain the solution of different kinds of algebraic equations, the nature of the solutions, and the interplay between geometry and algebra
Algebraic Geometry
Algebraic Geometry - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Algebraic Geometry write by Robin Hartshorne. This book was released on 2013-06-29. Algebraic Geometry available in PDF, EPUB and Kindle. An introduction to abstract algebraic geometry, with the only prerequisites being results from commutative algebra, which are stated as needed, and some elementary topology. More than 400 exercises distributed throughout the book offer specific examples as well as more specialised topics not treated in the main text, while three appendices present brief accounts of some areas of current research. This book can thus be used as textbook for an introductory course in algebraic geometry following a basic graduate course in algebra. Robin Hartshorne studied algebraic geometry with Oscar Zariski and David Mumford at Harvard, and with J.-P. Serre and A. Grothendieck in Paris. He is the author of "Residues and Duality", "Foundations of Projective Geometry", "Ample Subvarieties of Algebraic Varieties", and numerous research titles.
