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Arithmetic and Geometry
Arithmetic and Geometry presents highlights of recent work in arithmetic algebraic geometry by some of the world's leading mathematicians. Together, these 2016 lectures—which were …
Arithmetic Compactifications of PEL-Type Shimura Varieties
By studying the degeneration of abelian varieties with PEL structures, this book explains the compactifications of smooth integral models of all PEL-type Shimura varieties, …
Lectures on the Arithmetic Riemann-Roch Theorem. (AM-127), Volume 127
The arithmetic Riemann-Roch Theorem has been shown recently by Bismut-Gillet-Soul. The proof mixes algebra, arithmetic, and analysis. The purpose of this book is to give a concise …
Lectures on the Arithmetic Riemann-Roch Theorem. (AM-127), Volume 127
The arithmetic Riemann-Roch Theorem has been shown recently by Bismut-Gillet-Soul. The proof mixes algebra, arithmetic, and analysis. The purpose of this book is to give a concise …
Profinite Groups, Arithmetic, and Geometry. (AM-67), Volume 67
In this volume, the author covers profinite groups and their cohomology, Galois cohomology, and local class field theory, and concludes with a treatment of duality. His objective …
Arithmetic Moduli of Elliptic Curves. (AM-108), Volume 108
This work is a comprehensive treatment of recent developments in the study of elliptic curves and their moduli spaces. The arithmetic study of the moduli spaces began with Jacobi's …
Some Problems of Unlikely Intersections in Arithmetic and Geometry (AM-181)
This book considers the so-called Unlikely Intersections, a topic that embraces well-known issues, such as Lang's and Manin-Mumford's, concerning torsion points in subvarieties of …
Introduction to Arithmetic Theory of Automorphic Functions
The theory of automorphic forms is playing increasingly important roles in several branches of mathematics, even in physics, and is almost ubiquitous in number theory. This book …
Predicative Arithmetic. (MN-32)
This book develops arithmetic without the induction principle, working in theories that are interpretable in Raphael Robinson's theory Q. Certain inductive formulas, the bounded …
Arithmetic Compactifications of PEL-Type Shimura Varieties
By studying the degeneration of abelian varieties with PEL structures, this book explains the compactifications of smooth integral models of all PEL-type Shimura varieties, …