The isogeny conjecture for A-motives

• 成果类型: Article
• 署名作者: Pink, Richard
• 署名单位: Swiss Federal Institutes of Technology Domain; ETH Zurich
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-011-0357-0
• 发表日期: 2012
• 页码: 659-711
• 关键词: drinfeld-modules; t-motives; tate-conjecture; vector bundles; FIELDS; semisimplicity; FINITENESS; VARIETIES

摘要

We prove the isogeny conjecture for A-motives over finitely generated fields K of transcendence degree <= 1. This conjecture says that for any semisimple A-motive M over K, there exist only finitely many isomorphism classes of A-motives M' over K for which there exists a separable isogeny M' -> M. The result is in precise analogy to known results for abelian varieties and for Drinfeld modules and will have strong consequences for the p-adic and adelic Galois representations associated to M. The method makes essential use of the Harder-Narasimhan filtration for locally free coherent sheaves on an algebraic curve.