Refined abelian Stark conjectures and the equivariant leading term conjecture of Burns

DOI10.1112/S0010437X14007416zbMath1311.11108arXiv1406.4623OpenAlexW2964193159WikidataQ122919296 ScholiaQ122919296MaRDI QIDQ2935406

Takamichi Sano

Publication date: 29 December 2014

Published in: Compositio Mathematica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1406.4623

zbMATH Keywords

Artin \(L\)-seriesequivariant Tamagawa number conjectureRubin-Stark conjectureStark conjecturesDarmon's conjecture

Mathematics Subject Classification ID

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

Related Items (10)

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 \(s = 0\) ⋮ On generalised Kummer congruences and higher rank Iwasawa theory at arbitrary weights ⋮ A generalization of Darmon's conjecture for Euler systems for general \(p\)-adic representations ⋮ On Euler systems for the multiplicative group over general number fields ⋮ The equivariant Tamagawa number conjecture for abelian extensions of imaginary quadratic fields ⋮ Congruences for critical values of higher derivatives of twisted Hasse–Weil $L$-functions, II ⋮ Construction of elliptic \(\mathfrak{p}\)-units ⋮ On Stark elements of arbitrary weight and their \(p\)-adic families

Cites Work

• On the equivariant Tamagawa number conjecture for Tate motives
• 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
• On the cyclotomic main conjecture for the prime 2
• A class number formula for higher derivatives of abelian L-functions
• Thaine's Method for Circular Units and a Conjecture of Gross

This page was built for publication: Refined abelian Stark conjectures and the equivariant leading term conjecture of Burns