Tannakian duality for Anderson-Drinfeld motives and algebraic independence of Carlitz logarithms

Abstract

We develop a theory of Tannakian Galois groups for t-motives and relate this to the theory of Frobenius semilinear difference equations. We show that the transcendence degree of the period matrix associated to a given t-motive is equal to the dimension of its Galois group. Using this result we prove that Carlitz logarithms of algebraic functions that are linearly independent over the rational function field are algebraically independent.

39 pages

References in corpus (2)

• Determination of the algebraic relations among special Gamma-values in positive characteristic
• Uniformizable families of $t$-motives

Cited by in corpus (49)

• Linear independence of monomials of multizeta values in positive characteristic
• Values of certain L-series in positive characteristic
• Special L-values of Drinfeld modules
• A rapid introduction to Drinfeld modules, $t$-modules, and $t$-motives
• Multizeta values for F_q[t], their period interpretation and relations between them
• Artin t-Motifs
• Local Shtukas, Hodge-Pink Structures and Galois Representations
• The de Rham isomorphism for Drinfeld modules over Tate algebras
• Hyperderivatives of periods and quasi-periods for Anderson $t$-modules
• tau-recurrent sequences and modular forms
• Periods of $t$-modules as special values
• Pure Anderson Motives and Abelian τ-Sheaves
• Frobenius difference equations and algebraic independence of zeta values in positive equal characteristic
• Algebraic relations among periods and logarithms of rank 2 Drinfeld modules
• $h^1\ne h_1$ for Anderson t-motives
• Taylor coefficients of Anderson-Thakur series and explicit formulae
• Algebraic independence of the Carlitz period and its hyperderivatives
• A Difference Version of Nori's Theorem
• Linear relations among double zeta values in positive characteristic
• Vectorial Drinfeld modular forms over Tate algebras
• Pure Anderson Motives and Abelian Sheaves over Finite Fields
• Algebraic relations among hyperderivatives of periods and logarithms of Drinfeld modules
• Analytic continuation of multiple polylogarithms in positive characteristic
• Alternating multizeta values in positive characteristic
• Anderson t-modules with thin t-adic Galois representations
• Algebraic independence of values of Goss L-functions at s=1
• Geometric Gamma values and zeta values in positive characteristic
• Linear equations on Drinfeld modules
• On Furusho's analytic continuation of Drinfeld logarithms
• Hopf algebras and multiple zeta values in positive characteristic
• Algebraic independence of arithmetic gamma values and Carlitz zeta values
• Drinfeld $A$-quasi-modular forms
• Taylor coefficients of Anderson generating functions and Drinfeld torsion extensions
• Periods of third kind for rank 2 Drinfeld modules and algebraic independence of logarithms
• Analytic continuation of Kochubei multiple polylogarithms and its applications
• Algebraic independence of the Carlitz period and the positive characteristic multizeta values at n and (n,n)
• Identities for Anderson generating functions for Drinfeld modules
• On v-adic periods of t-motives
• Algebra structure of multiple zeta values in positive characteristic
• A $t$-motivic interpretation of shuffle relations for multizeta values
• On certain families of Drinfeld quasi-modular forms
• The analytic theory of vectorial Drinfeld modular forms
• On finite Carlitz multiple polylogarithms
• On lower bounds of the dimensions of multizeta values in positive characteristic
• Abelian equals A-finite for Anderson A-modules
• On the transcendence of special values of Goss $L$-functions attached to Drinfeld modules
• Universal Families of Eulerian Multiple Zeta Values in Positive Characteristics
• Hyperdifferential properties of Drinfeld quasi-modular forms
• Linear relations among algebraic points on tensor powers of the Carlitz module