Refined class number formulas for \(\mathbb{G}_m\)

DOI10.5802/jtnb.934zbMath1414.11155arXiv1312.4053OpenAlexW2963328059MaRDI QIDQ284486

Karl Rubin, Barry Mazur

Publication date: 18 May 2016

Published in: Journal de Théorie des Nombres de Bordeaux (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1312.4053

zbMATH Keywords

class number formulasEuler systems$L$-functionsKolyvagin systemsStark conjectures

Mathematics Subject Classification ID

Units and factorization (11R27) Class numbers, class groups, discriminants (11R29) Zeta functions and (L)-functions of number fields (11R42) Iwasawa theory (11R23)

Related Items (8)

Controlling Selmer groups in the higher core rank case ⋮ On the non-critical exceptional zeros of Katz \(p\)-adic \(L\)-functions for CM fields ⋮ On Iwasawa theory, zeta elements for \(\mathbb G_m\), and the equivariant Tamagawa number conjecture ⋮ On derivatives of \(p\)-adic \(L\)-series at \(s = 0\) ⋮ The equivariant Tamagawa number conjecture for abelian extensions of imaginary quadratic fields ⋮ The work of Barry Mazur ⋮ Congruences for critical values of higher derivatives of twisted Hasse–Weil $L$-functions, II ⋮ On Stark elements of arbitrary weight and their \(p\)-adic families

Cites Work

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• Controlling Selmer groups in the higher core rank case
• A generalization of Darmon's conjecture for Euler systems for general \(p\)-adic representations
• The Stark conjectures on Artin \(L\)-functions at \(s=0\). Lecture notes of a course in Orsay edited by Dominique Bernardi and Norbert Schappacher.
• Refined conjectures of the ``Birch and Swinnerton-Dyer type
• The refined \(\mathfrak p\)-adic abelian Stark conjecture in function fields
• Systèmes d'Euler \(p\)-adiques et théorie d'Iwasawa. (\(p\)-adic Euler systems and Iwasawa theory.)
• A Stark conjecture ``over \({\mathbb{Z}}\) for abelian \(L\)-functions with multiple zeros
• Congruences between derivatives of abelian \(L\)-functions at \(s =0\)
• Refined class number formulas and Kolyvagin systems
• Kolyvagin systems of Stark units
• Kolyvagin systems
• Thaine's Method for Circular Units and a Conjecture of Gross
• Euler Systems

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