Geometric main conjectures in function fields

DOI10.1515/crelle-2024-0069MaRDI QIDQ6658013

Cristian D. Popescu, Werner Bley

Publication date: 8 January 2025

Published in: Journal für die Reine und Angewandte Mathematik (Search for Journal in Brave)

Mathematics Subject Classification ID

Arithmetic theory of algebraic function fields (11R58) Cyclotomic function fields (class groups, Bernoulli objects, etc.) (11R60) Zeta functions and (L)-functions of number fields (11R42) Iwasawa theory (11R23) Integral representations related to algebraic numbers; Galois module structure of rings of integers (11R33) Zeta and (L)-functions in characteristic (p) (11M38)

Cites Work

• Multiplicative independence in function fields
• Projective modules
• The Stark conjectures on Artin \(L\)-functions at \(s=0\). Lecture notes of a course in Orsay edited by Dominique Bernardi and Norbert Schappacher.
• Formal Drinfeld modules.
• Fitting ideals of class groups in Carlitz-Hayes cyclotomic extensions
• Picard 1-motives and Tate sequences for function fields
• Stickelberger series and main conjecture for function fields
• Iwasawa main conjecture for the Carlitz cyclotomic extension and applications
• On the unique factorization theorem for formal power series
• Classifications of countably-based abelian profinite groups
• The Galois Module Structure of ℓ-adic Realizations of Picard 1-motives and Applications
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