$t$-Motives
Subtitle: Hodge Structures, Transcendence and Other Motivic Aspects
By: Gebhard Böckle, David Goss, Urs Hartl, Matthew A. Papanikolas
Series: EMS Series of Congress Reports; EMS series of congress reports
Publisher: European Mathematical Society Publishing House
Published: 2020
Place of publication: Zuerich, Switzerland
Language: eng
Format: [electronic resource] /
Number of pages: 473
ISBN-13: 9783037196984; 9783037191989
Subjects: Algebraic Geometry; Hodge theory; Géométrie algébrique; Théorie de Hodge; Number theory; Commutative rings and algebras
Description: This volume contains research and survey articles on Drinfeld modules, Anderson $t$-modules and $t$-motives. Much material that had not been easily accessible in the literature is presented here, for example the cohomology theories and Pink's theory of Hodge structures attached to Drinfeld modules and $t$-motives. Also included are survey articles on the function field analogue of Fontaine's theory of $p$-adic crystalline Galois representations and on transcendence methods over function fields, encompassing the theories of Frobenius difference equations, automata theory, and Mahler's method. In addition, this volume contains a small number of research articles on function field Iwasawa theory, 1-$t$-motifs, and multizeta values.This book is a useful source for learning important techniques and an effective reference for all researchers working in or interested in the area of function field arithmetic, from graduate students to established experts.
Notes: Includes bibliographical references and index.
Table of contents: title: A rapid introduction to Drinfeld modules, $t$-modules, and $t$-motives  -- W. Dale Brownawell, Matthew A. Papanikolas; title: Pink's theory of Hodge structures and the Hodge conjecture over function fields  -- Urs Hartl, Ann-Kristin Juschka; title: Local shtukas, Hodge-Pink structures and Galois representations  -- Urs Hartl, Wansu Kim; title: Frobenius difference equations and difference Galois groups  -- Chieh-Yu Chang; title: An introduction to Mahler's method for transcendence and algebraic independence  -- Federico Pellarin; title: Automata methods in transcendence  -- Dinesh S. Thakur; title: Aspects of Iwasawa theory over function fields  -- Andrea Bandini, Francesc Bars, Ignazio Longhi; title: 1-$t$-Motifs  -- Lenny Taelman; title: Multizeta in function field arithmetic -- Dinesh S. Thakur.