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

• 成果类型: Article
• 署名作者: Papanikolas, Matthew A.
• 署名单位: Texas A&M University System; Texas A&M University College Station
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-007-0073-y
• 发表日期: 2008
• 页码: 123-174
• 关键词: t-motives; transcendence; periods; FIELDS; VALUES

摘要

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.