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$t$-Motives: Hodge Structures, Transcendence and Other Motivic Aspects
EMS Series of Congress Reports

$t$-Motives: Hodge Structures, Transcendence and Other Motivic Aspects

Gebhard Böckle (Universität Heidelberg, Germany)
David Goss
Urs Hartl (Universität Münster, Germany)
Matthew A. Papanikolas (Texas A&M University, College Station, USA)

ISBN print 978-3-03719-198-9, ISBN online 978-3-03719-698-4
DOI 10.4171/198
May 2020, 473 pages, hardcover, 17 x 24 cm.
89.00 Euro

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.

Keywords: Drinfeld modules, $t$-motives, Anderson $t$-modules, transcendence, Hodge-Pink-structures