\(p\)-adic regulators on curves and special values of \(p\)-adic \(L\)-functions

DOI10.1007/BF01394332zbMath0655.14010WikidataQ56813947 ScholiaQ56813947MaRDI QIDQ1109091

Ehud de Shalit, Robert F. Coleman

Publication date: 1988

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/143596

zbMATH Keywords

complex multiplicationp-adic L-functionlogarithmic F-crystalp-adic analytic integration theoryp-adic regulator mapp-adic version of the Beilinson conjectureswide open rigid analytic spaces

Mathematics Subject Classification ID

Arithmetic ground fields for curves (14H25) Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture) (14G10) Local ground fields in algebraic geometry (14G20) Complex multiplication and abelian varieties (14K22) Applications of methods of algebraic (K)-theory in algebraic geometry (14C35)

Related Items (25)

Obituary: Robert F. Coleman 1954--2014 ⋮ A short proof of de Shalit's cup product formula ⋮ Higher regulators and Hecke \(L\)-series of imaginary quadratic fields. I ⋮ The Hyodo-Kato structure for curves ⋮ \(p\)-adic Eisenstein-Kronecker series and non-critical values of \(p\)-adic Hecke \(L\)-function of an imaginary quadratic field when the conductor is divisible by \(p\) ⋮ \(p\)-adic heights and Vologodsky integration ⋮ Explicit Vologodsky integration for hyperelliptic curves ⋮ Explicit Coleman integration in larger characteristic ⋮ Explicit Coleman integration for curves ⋮ Vologodsky integration on curves with semi-stable reduction ⋮ The universal vectorial bi-extension and \(p\)-adic heights ⋮ The Frobenius and monodromy operators for curves and abelian varieties ⋮ On integrality of \(p\)-adic iterated integrals ⋮ Riemann-Hurwitz formula for finite morphisms of \(p\)-adic curves ⋮ Syntomic regulators and \(p\)-adic integration. I: Rigid syntomic regulators ⋮ Syntomic regulators and \(p\)-adic integration. II: \(K_2\) of curves ⋮ On the syntomic regulator for \(K_1\) of a surface ⋮ Explicit Coleman Integration for Hyperelliptic Curves ⋮ Kato's Euler system and rational points on elliptic curves. I: A \(p\)-adic Beilinson formula ⋮ The syntomic regulator for the K-theory of fields ⋮ Unnamed Item ⋮ \(p\)-adic polylogarithms and \(p\)-adic Hecke \(L\)-functions for totally real fields ⋮ Coleman integration for even-degree models of hyperelliptic curves ⋮ \(p\)-adic Arakelov theory ⋮ On the \(p\)-adic realization of elliptic polylogarithms for CM-elliptic curves

Cites Work

• p-adic K-theory of elliptic curves
• Stable reduction and uniformization of abelian varieties. I
• Dilogarithms, regulators and \(p\)-adic \(L\)-functions
• Torsion points on curves and p-adic abelian integrals
• Higher regulators and values of \(L\)-functions
• Higher regulators and values of L-functions of curves
• \(p\)-adic interpolation of real analytic Eisenstein series
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