Extremely carefully written, masterfully thought out, and skillfully arranged introduction ... to the arithmetic of algebraic curves, on the one hand, and to the algebro-geometric aspects of number theory, on the other hand. ... an excellent guide for beginners in arithmetic geometry, just as an interesting reference and methodical inspiration for teachers of the subject ... a highly welcome addition to the existing literature. --Zentralblatt MATH The interaction between number theory and algebraic geometry has been especially fruitful. In this volume, the author gives a unified presentation of some of the basic tools and concepts in number theory, commutative algebra, and algebraic geometry, and for the first time in a book at this level, brings out the deep analogies between them. The geometric viewpoint is stressed throughout the book. Extensive examples are given to illustrate each new concept, and many interesting exercises are given at the end of each chapter. Most of the important results in the one-dimensional case are proved, including Bombieri's proof of the Riemann Hypothesis for curves over a finite field. While the book is not intended to be an introduction to schemes, the author indicates how many of the geometric notions introduced in the book relate to schemes, which will aid the reader who goes to the next level of this rich subject.
... 2015 Peter S. Ozsváth, András I. Stipsicz, and Zoltán Szabó, Grid Homology for Knots and Links, 2015 Vladimir I. Bogachev, Nicolai V. Krylov, Michael Röckner, and Stanislav V. Shaposhnikov, Fokker–Planck–Kolmogorov Equations, ...
With many exercises, this book can be used as a text for a first course in number theory or for a subsequent course on arithmetic (or diophantine) geometry at the junior-senior level.
This book originated in the idea that open problems act as crystallization points in mathematical research. Mathematical books usually deal with fully developed theories.
Duke Math. J. 59 (1989), no. 3, pages 785–801. [9] Cassels, J. W. S., Flynn, E. V. Prolegomena to a Middlebrow Arithmetic of Curves of Genus 2, London Matematical Society Lecture Note Series 230, Cambridge University Press (1996).
... Mathematics, 2017 Erica Flapan, Allison Henrich, Aaron Kaestner, and Sam Nelson, Editors, Knots, Links, Spatial Graphs, and Algebraic Invariants, 2017 Jeffrey Bergen, Stefan Catoiu, and William Chin, Editors, Groups, Rings, Group Rings ...
This book is concerned with the dynamics of rational transformations of projective varieties and meromorphic transformations of compact Kahler manifolds.
This volume contains the proceedings of the Ninth International Conference on Finite Fields and Applications, held in Ireland, July 13-17, 2009. It includes survey papers by all invited speakers as well as selected contributed papers.