This volume contains the proceedings of the AMS Special Session on Higher Genus Curves and Fibrations in Mathematical Physics and Arithmetic Geometry, held on January 8, 2016, in Seattle, Washington. Algebraic curves and their fibrations have played a major role in both mathematical physics and arithmetic geometry. This volume focuses on the role of higher genus curves; in particular, hyperelliptic and superelliptic curves in algebraic geometry and mathematical physics. The articles in this volume investigate the automorphism groups of curves and superelliptic curves and results...

This book is a collection of articles on abelian varieties and number theory dedicated to Gerhard Frey's 75th birthday. It contains original articles by experts in the area of arithmetic and algebraic geometry.

The articles cover topics on Abelian varieties and finitely generated Galois groups, ranks of Abelian varieties and Mordell-Lang conjecture, Tate-Shafarevich group and isogeny volcanos, endomorphisms of superelliptic Jacobians, obstructions to local-global principles over semi-global fields, Drinfield modular variaties, representations of etale fundamental groups and...

Isogeny-based cryptography, built on the arithmetic of elliptic curves and higher-dimensional abelian varieties like abelian surfaces, is a cornerstone of post-quantum security. Abelian Surfaces and Isogeny-based Cryptography compiles cutting-edge research papers presented at a landmark conference held at the Einstein Institute of Mathematics, The Hebrew University of Jerusalem, from July 29–31, 2024, supported by the NATO Science for Peace and Security Programme. This event united mathematicians, cryptographers, and computer scientists to explore the interplay of algebraic geometry and...