Congruences between derivatives of geometric L-functions

• 成果类型: Article
• 署名作者: Burns, David
• 署名单位: University of London; King's College London
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-010-0286-3
• 发表日期: 2011
• 页码: 221-256
• 关键词: tamagawa number conjecture; abelian l-functions; stark conjecture; stickelberger elements; VARIETIES

摘要

We prove a natural refinement of a theorem of Lichtenbaum describing the leading terms of Zeta functions of curves over finite fields in terms of Weil-,tale cohomology. We then use this result to prove the validity of Chinburg's Omega(3)-Conjecture for all abelian extensions of global function fields, to prove natural refinements and generalisations of the refined Stark conjectures formulated by, amongst others, Gross, Tate, Rubin and Popescu, to prove a variety of explicit restrictions on the Galois module structure of unit groups and divisor class groups and to describe explicitly the Fitting ideals of certain Weil-,tale cohomology groups. In an Appendix coauthored with K.F. Lai and K.-S. Tan we also show that the main conjectures of geometric Iwasawa theory can be proved without using either crystalline cohomology or Drinfeld modules.