p-adic K-theory of elliptic curves
type: Item
instance of: scholarly article
title: p-adic K-theory of elliptic curves
zbMATH Open document ID: 0627.14010
DOI: 10.1215/S0012-7094-87-05415-9
published in: Duke Mathematical Journal
publication date: 1987-01-01T00:00:00Z
review text: The author proves some results on p-adic K-groups of a smooth variety over a number field F. In particular he shows that for a \(curve\quad X\) of genus \(g\) over F the dimension of \(K_ 2(X,{\mathbb{Q}}_ p/{\mathbb{Z}}_ p)\) is at least g[F:\({\mathbb{Q}}]\). The proof relies on comparison with the corresponding étale K-theory and results of \textit{W. G. Dwyer} and \textit{E. M. Friedlander} [Trans. Am. Math. Soc. 292, 247-280 (1985; Zbl 0581.14012)]. Examples are given for elliptic curves over an imaginary quadratic field such that \(\dim (K_ 2(X,{\mathbb{Q}}_ p/{\mathbb{Z}}_ p))=[F:{\mathbb{Q}}]\) for primes p satisfying certain regularity conditions. In the final section the author constructs higher p-adic regulator maps for certain elliptic curves and obtains a result on values of a p-adic L- function which can be seen as p-adic analog to results of Beilinson on the generalized conjecture of Birch and Swinnerton-Dyer.
Mathematics Subject Classification ID: 14C35
Mathematics Subject Classification ID: 14G25
Mathematics Subject Classification ID: 14G10
Mathematics Subject Classification ID: 14H25
Mathematics Subject Classification ID: 14H52
Mathematics Subject Classification ID: 14H45
zbMATH DE Number: 4019207
zbMATH Keywords: p-adic K-groups of a smooth variety
zbMATH Keywords: elliptic curves
zbMATH Keywords: higher p-adic regulator maps
zbMATH Keywords: values of a p-adic L-function
zbMATH Keywords: generalized conjecture of Birch and Swinnerton-Dyer
author: Christophe Soulé
reviewed by: Frank Herrlich
MaRDI profile type: Publication
cites work: Higher regulators and values of \(L\)-functions
cites work: Q3876042
cites work: Gersten's conjecture and the homology of schemes
cites work: On the conjecture of Birch and Swinnerton-Dyer
cites work: Q3739326
cites work: Arithmetic on elliptic curves with complex multiplication. With an appendix by B. Mazur
cites work: \(p\)-adic interpolation of real analytic Eisenstein series
cites work: Q4177670
cites work: $ K$-COHOMOLOGY OF SEVERI-BRAUER VARIETIES AND THE NORM RESIDUE HOMOMORPHISM
cites work: Primary homotopy theory
cites work: Higher algebraic K-theory: I
cites work: Q5617480
cites work: On higher p-adic regulators
cites work: Q4294448
cites work: Q4744388
cites work: Opérations En K-Théorie Algébrique
cites work: Q3717201
cites work: Q4770461
cites work: Q5332675
cites work: Riemann-Roch for algebraic versus topological K-theory
cites work: Q3724525
cites work: Q4742884
cites work: On two variable p-adic L-functions
full work available at URL: s0012-7094-87-05415-9
OpenAlex ID: W1590953788
description: scientific article; zbMATH DE number 4019207