Arithmetic representations of fundamental groups I

• 成果类型: Article
• 署名作者: Litt, Daniel
• 署名单位: Columbia University
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-018-0810-4
• 发表日期: 2018
• 页码: 605-639
• 关键词: adic iterated integrals; complex function-fields; open image theorem; galois actions; abelian-varieties; level structures; conjecture; CURVES; coverings

摘要

Let X be a normal algebraic variety over a finitely generated field k of characteristic zero, and let be a prime. Say that a continuous adic representation of et 1 (X k) is arithmetic if there exists a finite extension k of k, and a representation. of p et 1 (Xk ), with. a subquotient of. p1(Xk). We show that there exists an integer N = N(X) such that every nontrivial, semisimple arithmetic representation of p et 1 (X) is nontrivial mod N. As a corollary, we prove that any nontrivial - adic representation of pet 1 (X) which arises from geometry is nontrivial mod l(N).