On the additive dilogarithm

Ünver, Sinan

doi:10.2140/ant.2009.3.1

Cited by 10 publications

(18 citation statements)

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“…Such a construction was made by Bloch and Esnault [4] in the slightly different context of additive Chow groups in weight two. This construction was the main motivation for [21] where additive dilogarithms over k[ε] 2 was constructed. This note can be considered as a generalization of [21] to higher weights.…”

Section: Outlinementioning

confidence: 99%

“…This construction was the main motivation for [21] where additive dilogarithms over k[ε] 2 was constructed. This note can be considered as a generalization of [21] to higher weights. We briefly sketch the contents of the paper.…”

Section: Outlinementioning

confidence: 99%

“…Section 3 is the main part of the construction where a lifting to k[ε] n+1 argument is used as in [21] to define the polylogarithm. In Definition 1, a formula for li n is given in terms of (n+1) n .…”

Section: Outlinementioning

confidence: 99%

“…In Sect. 4.2, we use the context of functional equations of additive polylogarithms to prove that the additive dilogarithm and its higher modulus generalizations in [21] satisfy Wojtkowiak's functional equations.…”

Section: Outlinementioning

confidence: 99%

“…For more information on motivic cohomology as it relates to the discussion below, see the introduction of [21] and the references therein.…”

mentioning

confidence: 99%

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Additive polylogarithms and their functional equations

Ünver

2010

Math. Ann.

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Let k[ε] 2 := k[ε]/(ε 2 ). The single valued real analytic n-polylogarithm L n : C → R is fundamental in the study of weight n motivic cohomology over a field k, of characteristic 0. In this paper, we extend the construction in Ünver (Algebra Number Theory 3:1-34, 2009) to define additive n-polylogarithms li n :k[ε] 2 → k and prove that they satisfy functional equations analogous to those of L n . Under a mild hypothesis, we show that these functions descend to an analog of the nth Bloch group B n (k[ε] 2 ) defined by Goncharov (Adv Math 114:197-318, 1995). We hope that these functions will be useful in the study of weight n motivic cohomology over k[ε] 2 .

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Section: Outlinementioning

confidence: 99%

Section: Outlinementioning

confidence: 99%

Section: Outlinementioning

confidence: 99%

Section: Outlinementioning

confidence: 99%

“…For more information on motivic cohomology as it relates to the discussion below, see the introduction of [21] and the references therein.…”

mentioning

confidence: 99%