Abelian Varieties and Number Theory

ISBN-13: 9781470452070 / Angielski / Miękka / 2021 / 210 str.

Moshe Jarden;Tony Shaska

Opis

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 specialization of algebraic cycles, Deuring's theory of constant reductions, etc.

The book will be a valuable resource to graduate students and experts working on Abelian varieties and related areas.

Spis treści

• B.-H. Im and M. Larsen, Abelian varieties and finitely generated Galois groups
• A. Fehm and S. Petersen, Ranks of abelian varieties and the full Mordell-Lang conjecture in dimension one
• J. A. Antoniadis and A. Kontogeorgis, The group of automorphisms of the Heisenberg curve
• C. Creutz and J. F. Voloch, Tate-Shafarevich groups of constant elliptic curves and isogeny volcanoes
• Y. Zarhin, Endomorphisms of ordinary superelliptic Jacobians
• B. Green and P. Roquette, An introduction to Deuring's theory of constant reductions
• D. Rossler, Purely inseparable points on curves
• A. Tamagawa, Correspondences on curves in positive characteristic
• A. Fehm, D. Haran, and E. Paran, The inverse Galois problem over $\mathbb(z)$
• L. Bary-Soroker and A. Entin, Explicit Hilbert's irreducibility theorem in function fields
• D. Harbater, J. Hartmann, V. Karemaker, and F. Pop, A comparison between obstructions to local-global principles over semi-global fields
• G. Bockle and F. Breuer, The generic monodromy of Drinfeld modular varieties in special characteristic
• A. Razon, Symmetric tensor products of octonion algebras
• A. Cadoret, Representations of etale fundamental groups and specialization of algebraic cycles