The Additive Dilogarithm
نویسنده
چکیده
A notion of additive dilogarithm for a field k is introduced, based on the K-theory and higher Chow groups of the affine line relative to 2(0). Analogues of the K2-regulator, the polylogarithm Lie algebra, and the `-adic realization of the dilogarithm motive are discussed. The higher Chow groups of 0-cycles in this theory are identified with the Kähler differential forms Ωk. It is hoped that these results will serve as a guide in developing a theory of contravariant motivic cohomology with modulus, modelled on the generalized Jacobians of Rosenlicht and Serre.
منابع مشابه
Algebraic Cycles and Additive Dilogarithm
For an algebraically closed field k of characteristic 0, we give a cycle-theoretic description of the additive 4-term motivic exact sequence associated to the additive dilogarithm of J.-L. Cathelineau, that is the derivative of the Bloch-Wigner function, via the cubical additive higher Chow groups under one assumption. The 4-term functional equation of Cathelineau, an additive analogue of the A...
متن کاملDilogarithm in Integrable Systems
We discuss some curious aspects of the Rogers dilogarithm appearing in integrable systems in two dimensions.
متن کاملSums of Series of Rogers Dilogarithm Functions
Some sums of series of Rogers dilogarithm functions are established by Abel’s functional equation.
متن کاملA proof of the pentagon relation for the quantum dilogarithm
1 Introduction The quantum dilogarithm function is given by the following integral: Φ h (z) := exp − 1 4 Ω e −ipz sh(πp)sh(πhp) dp p , sh(p) = e p − e −p 2. Here Ω is a path from −∞ to +∞ making a little half circle going over the zero. So the integral is convergent. It goes back to Barnes [Ba], and appeared in many papers during the last 30 years: • The function Φ h (z) is meromorphic with pol...
متن کاملCluster algebras and derived categories
This is an introductory survey on cluster algebras and their (additive) categorification using derived categories of Ginzburg algebras. After a gentle introduction to cluster combinatorics, we review important examples of coordinate rings admitting a cluster algebra structure. We then present the general definition of a cluster algebra and describe the interplay between cluster variables, coeff...
متن کامل