tt-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
t-Motives: Hodge Structures, Transcendence and Other Motivic Aspects cover
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This volume contains research and survey articles on Drinfeld modules, Anderson tt-modules and tt-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 tt-motives. Also included are survey articles on the function field analogue of Fontaine’s theory of pp-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-tt-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.