Research Project: Artin Yerel Halkları ve P-adik Cisimler Üzerinde Karmaşık Tate Motifleri: Regülatörlerin İnşası ve Periyotlar Arasındaki İlişkiler
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Contributors
Funders
ID
TB.00025
Authors
Ünver, Sinan
Faculty Member
Publications
Additive polylogarithms and their functional equations
(Springer, 2010) Ünver, Sinan; Department of Mathematics; Yes; College of Sciences
Let k[epsilon](2) := k[epsilon]/(epsilon(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 Unver (Algebra Number Theory 3:1-34, 2009) to define additive n-polylogarithms li(n):k[epsilon](2) -> k and prove that they satisfy functional equations analogous to those of Ln. Under a mild hypothesis, we show that these functions descend to an analog of the nth Bloch group B'(n)(k[epsilon](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[epsilon](2).
Deformations of Bloch groups and Aomoto dilogarithms in characteristic p
(Academic Press Inc , 2011) Ünver, Sinan; Department of Mathematics; Yes; College of Sciences
In this paper, we study the Bloch group B-2(F[epsilon](2)) over the ring of dual numbers of the algebraic closure of the field with p elements, for a prime p >= 5. We show that a slight modification of Kontsevich's 11/2-logarithm defines a function on B-2(F[epsilon](2)). Using this function and the characteristic p version of the additive dilogarithm function that we previously defined, we determine the structure of the infinitesimal part of B-2(Ff[epsilon](2)) completely. This enables us to define invariants on the group of deformations of Aomoto dilogarithms and determine its structure. This final result might be viewed as the analog of Hilbert's third problem in characteristic p.
