Syntomic regulators andp-adic integration I: Rigid syntomic regulators

Besser, Amnon

doi:10.1007/bf02834843

Cited by 69 publications

(130 citation statements)

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“…In order to adapt our calculations to Besser's in [Bes2] and [Bes3], it will be convenient to fix a particular choice of polynomial P and form P . (In the next section we shall exploit the fact that the computations performed there hold independently of the choice of P , and will work with a different polynomial so that we can take advantadge of the results obtained in [DR].)…”

Section: Wherementioning

confidence: 99%

“…Although a more optimal choice for P Eχ (t) would have been the linear polynomial t − χ(p)p, we made here a choice corresponding to the one made in the definition of the modified syntomic regulator reg(u χ ) of the function u χ (cf. [Bes2,Prop. 10.3]).…”

Section: Wherementioning

confidence: 99%

“…This way F Eχ also equals the modified syntomic regulator reg(u χ ) of u χ defined in [Bes2,Prop. 10.3].…”

Section: Wherementioning

confidence: 99%

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Beilinson-Flach elements and Euler systems I: Syntomic regulators and 𝑝-adic Rankin 𝐿-series

Bertolini

Darmon

Rotger³

2014

J. Algebraic Geom.

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This article is the first in a series devoted to the Euler system arising from p-adic families of Beilinson-Flach elements in the first K-group of the product of two modular curves. It relates the image of these elements under the p-adic syntomic regulator (as described by Besser [Bes3]) to the special values at the near-central point of Hida's p-adic Rankin L-function attached to two Hida families of cusp forms.

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Section: Wherementioning

confidence: 99%

Section: Wherementioning

confidence: 99%

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Beilinson-Flach elements and Euler systems I: Syntomic regulators and 𝑝-adic Rankin 𝐿-series

Bertolini

Darmon

Rotger³

2014

J. Algebraic Geom.

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“…where ch syn is the syntomic Chern character [Gro94,Niz97,Bes00b]. We recall that the regulator is easily derived from the Chern character.…”

Section: Introductionmentioning

confidence: 99%

On the syntomic regulator for K 1 of a surface

Besser

2011

Isr. J. Math.

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Abstract. We consider elements of K 1 (S), where S is a proper surface over a p-adic field with good reduction, which are given by a formal sum (Z i , f i ) with Z i curves in S and f i rational functions on the Z i in such a way that the sum of the divisors of the f i is 0 on S. Assuming compatibility of pushforwards in syntomic and motivic cohomologies our result computes the syntomic regulator of such an element, interpreted as a functional on H 2 dR (S), when evaluated on the cup product ω ∪ [η] of a holomorphic form ω by the first cohomology class of a form of the second kind η. The result is i Fη, log(f i ); Fω gl,Z i , where Fω and Fη are Coleman integrals of ω and η respectively and the symbol in brackets is the global triple index, as defined in our previous work.

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“…Thus one might hope that the relative Chern character gives a unifying frame for the study of both, classical and p-adic, regulators. Since the p-adic analogue of Beilinson's regulator is the rigid syntomic regulator [2] there should also be a comparison result for Karoubi's relative Chern character and the syntomic regulator for smooth varieties over a p-adic field. So far this is not known in general and in this paper we treat the case of a finite extension of Q p .…”

Section: Introductionmentioning

confidence: 99%