A reciprocity map and the two-variable \(p\)-adic \(L\)-function

DOI10.4007/annals.2011.173.1.7zbMath1248.11085arXiv0709.3591OpenAlexW2136845501MaRDI QIDQ640743

Romyar T. Sharifi

Publication date: 20 October 2011

Published in: Annals of Mathematics. Second Series (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0709.3591

zbMATH Keywords

Iwasawa theorymodular symbolscyclotomic unitscup productsEisenstein idealp-adic L function

Mathematics Subject Classification ID

Special values of automorphic (L)-series, periods of automorphic forms, cohomology, modular symbols (11F67) Iwasawa theory (11R23) Galois cohomology (11R34)

Related Items (19)

On Sharifi’s conjecture: Exceptional case ⋮ Modular symbols and the integrality of zeta elements ⋮ \( \mu \)-type subgroups of \(J_1(N)\) and application to cyclotomic fields ⋮ New criteria for Vandiver's conjecture using Gauss sums -- heuristics and numerical experiments ⋮ Reciprocity maps with restricted ramification ⋮ Level compatibility in Sharifi’s conjecture ⋮ Algebraic number theory. Abstracts from the workshop held June 25--30, 2023 ⋮ Ordinary pseudorepresentations and modular forms ⋮ On congruence modules related to Hilbert Eisenstein series ⋮ Congruences with Eisenstein series and -invariants ⋮ Level compatibility in the passage from modular symbols to cup products ⋮ The Eisenstein ideal with squarefree level ⋮ The geometry of Hida families II: -adic -modules and -adic Hodge theory ⋮ Towards a conjecture of Sharifi ⋮ The geometry of Hida families I: \(\Lambda\)-adic de Rham cohomology ⋮ Hida duality and the Iwasawa main conjecture ⋮ Modular Symbols in Iwasawa Theory ⋮ On Equivariant Characteristic Ideals of Real Classes ⋮ On the failure of Gorensteinness at weight 1 Eisenstein points of the eigencurve

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Arithmetic on modular curves
• Class fields of abelian extensions of \(\mathbb Q\)
• Iwasawa theory and the Eisenstein ideal
• Galois representations into \(\text{GL}_2(\mathbb Z_pX)\) attached to ordinary cusp forms.
• Modular forms in characteristic \(\ell\) and special values of their \(L\)-functions
• On the arithmetic of special values of L functions
• Coleman power series for \(K_2\) and \(p\)-adic zeta functions of modular forms
• A cup product in the Galois cohomology of number fields
• Ordinary \(p\)-adic étale cohomology groups attached to towers of elliptic modular curves. II
• \(p\)-adic \(L\)-functions and \(p\)-adic periods of modular forms
• On some modules in the theory of cyclotomic fields
• Companion forms and the structure of \(p\)-adic Hecke algebras. II
• The Steinberg symbol and special values of $L$-functions
• Iwasawa modules attached to congruences of cusp forms
• Un sous-groupe $p$-divisible de la jacobienne de $X_1(N p_r)$ comme module sur l'algèbre de Hecke
• Congruence modules related to Eisenstein series
• On the p-adic Eichler-Shimura isomorphism for Λ-adic cusp forms.
• Companion forms and the structure ofp-adic Hecke algebras

This page was built for publication: A reciprocity map and the two-variable \(p\)-adic \(L\)-function