This article is the first in a series devoted to Kato's Euler system arising from p-adic families of Beilinson elements in the K-theory of modular curves. It proves a p-adic Beilinson formula relating the syntomic regulator (in the sense of Coleman-de Shalit and Besser) of certain distinguished elements in the K-theory of modular curves to the special values at integer points a parts per thousand yen 2 of the Mazur-Swinnerton-Dyer p-adic L-function attached to cusp forms of weight 2. When combined with the explicit relation between syntomic regulators and p-adic ,tale cohomology, this leads to an alternate proof of the main results of [Br2] and [Ge] which is independent of Kato's explicit reciprocity law.

Kato's Euler system and rational points on elliptic curves I : A p-adic Beilinson formula / M. Bertolini, H. Darmon. - In: ISRAEL JOURNAL OF MATHEMATICS. - ISSN 0021-2172. - 199:1(2013), pp. 163-188. [10.1007/s11856-013-0047-2]

Kato's Euler system and rational points on elliptic curves I : A p-adic Beilinson formula

M. Bertolini;
2013

Abstract

This article is the first in a series devoted to Kato's Euler system arising from p-adic families of Beilinson elements in the K-theory of modular curves. It proves a p-adic Beilinson formula relating the syntomic regulator (in the sense of Coleman-de Shalit and Besser) of certain distinguished elements in the K-theory of modular curves to the special values at integer points a parts per thousand yen 2 of the Mazur-Swinnerton-Dyer p-adic L-function attached to cusp forms of weight 2. When combined with the explicit relation between syntomic regulators and p-adic ,tale cohomology, this leads to an alternate proof of the main results of [Br2] and [Ge] which is independent of Kato's explicit reciprocity law.
syntomic regulators; swinnerton-dyer; special values; zeta-functions; modular-forms; series; birch
Settore MAT/03 - Geometria
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/249520
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