Elliptic Curves and Arithmetic Invariants

DOI10.1007/978-1-4614-6657-4zbMath1284.11001OpenAlexW590793360MaRDI QIDQ4912507

Haruzo Hida

Publication date: 4 April 2013

Published in: Springer Monographs in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-1-4614-6657-4

zbMATH Keywords

modular formelliptic curveShimura curve\(p\)-adic \(L\)-functionHecke algebramodular curve\(\mu\)-invariantShimura varietyscheme theorycritical \(L\)-value\({\mathcal L}\)-invariant

Mathematics Subject Classification ID

Elliptic curves over global fields (11G05) Research exposition (monographs, survey articles) pertaining to number theory (11-02) Special values of automorphic (L)-series, periods of automorphic forms, cohomology, modular symbols (11F67) Complex multiplication and moduli of abelian varieties (11G15) Galois representations (11F80) Arithmetic aspects of modular and Shimura varieties (11G18) Modular and Shimura varieties (14G35) Iwasawa theory (11R23) Generalizations (algebraic spaces, stacks) (14A20)

Related Items (12)

p-Adic Analogues of the BSD Conjecture and the $$\mathcal {L}$$ -Invariant ⋮ \( \mu \)-type subgroups of \(J_1(N)\) and application to cyclotomic fields ⋮ \(\mathfrak p\)-rigidity and Iwasawa \(\mu\)-invariants ⋮ Quantitative non-vanishing of Dirichlet \(L\)-values modulo \(p\) ⋮ Central values of \(L\)-functions of cubic twists ⋮ ANDRÉ–OORT CONJECTURE AND NONVANISHING OF CENTRAL -VALUES OVER HILBERT CLASS FIELDS ⋮ ON THE NON-TRIVIALITY OF THE -ADIC ABEL–JACOBI IMAGE OF GENERALISED HEEGNER CYCLES MODULO , II: SHIMURA CURVES ⋮ Anticyclotomic \(p\)-adic \(L\)-functions and Ichino's formula ⋮ An \(l\neq p\)-interpolation of genuine \(p\)-adic \(L\)-functions ⋮ Local indecomposability of Tate modules of non-CM abelian varieties with real multiplication ⋮ On the non-triviality of the $p$-adic Abel–Jacobi image of generalised Heegner cycles modulo $p$, I: Modular curves ⋮ Control of $$\Lambda $$ -adic Mordell–Weil Groups

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