Algebraic independence of periods and logarithms of Drinfeld modules

DOI10.1090/S0894-0347-2011-00714-5zbMath1271.11079arXiv1005.5120WikidataQ60118146 ScholiaQ60118146MaRDI QIDQ3115809

Chieh-Yu Chang, Matthew A. Papanikolas

Publication date: 11 February 2012

Published in: Journal of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1005.5120

zbMATH Keywords

Drinfeld modulesperiodsalgebraic independencelogarithms

Mathematics Subject Classification ID

Drinfel'd modules; higher-dimensional motives, etc. (11G09) Transcendence theory of Drinfel'd and (t)-modules (11J93) Transcendence theory of elliptic and abelian functions (11J89)

Related Items

Prolongations of \(t\)-motives and algebraic independence of periods ⋮ Linear independence of monomials of multizeta values in positive characteristic ⋮ Algebraic independence of values of Goss \(L\)-functions at \(s=1\) ⋮ Effective rigid analytic trivializations for Drinfeld modules ⋮ Linear equations on Drinfeld modules ⋮ Algebraic relations among Goss’s zeta values on elliptic curves ⋮ A rapid introduction to Drinfeld modules, \(t\)-modules, and \(t\)-motives ⋮ Frobenius difference equations and difference Galois groups ⋮ On periods of the third kind for rank 2 Drinfeld module ⋮ On finite Carlitz multiple polylogarithms ⋮ Identities for Anderson generating functions for Drinfeld modules ⋮ An effective criterion for Eulerian multizeta values in positive characteristic ⋮ The de Rham isomorphism for Drinfeld modules over Tate algebras ⋮ Recent developments in the theory of Anderson modules ⋮ Periods of \(t\)-modules as special values ⋮ Tensor powers of rank 1 Drinfeld modules and periods ⋮ Special \(L\)-values of Drinfeld modules ⋮ Four exponentials conjecture of Drinfeld modules ⋮ Special \(L\)-values and shtuka functions for Drinfeld modules on elliptic curves ⋮ On Drinfeld modular forms of higher rank and quasi-periodic functions ⋮ Taylor coefficients of Anderson generating functions and Drinfeld torsion extensions ⋮ Anderson 𝑡-modules with thin 𝑡-adic Galois representations

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Transcendence and Drinfeld modules
• \(t\)-motives
• Hodge cycles, motives, and Shimura varieties
• Analytic homomorphisms into Drinfeld modules
• The Mumford-Tate conjecture for Drinfeld-modules
• Determination of the algebraic relations among special \(\Gamma\)-values in positive characteristic
• Tannakian duality for Anderson-Drinfeld motives and algebraic independence of Carlitz logarithms
• Algebraic relations among periods and logarithms of rank 2 Drinfeld modules
• Elliptic Functions and Transcendence
• On quasi-reductive group schemes
• On the de Rham isomorphism for Drinfeld modules.
• Linear independence of Gamma values in positive characteristic
• Minimal extensions of algebraic groups and linear independence