#### DOCUMENTA MATHEMATICA,
Extra Volume: Kazuya Kato's Fiftieth Birthday (2003), 131-155

** Spencer Bloch and Hélène Esnault **
The Additive Dilogarithm

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 $K_2$-regulator, the polylogarithm Lie algebra, and the
$\ell$-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 $\Omega^*_k$. 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.

2000 Mathematics Subject Classification: Primary 11G55

Keywords and Phrases:

Full text: dvi.gz 47 k,
dvi 124 k,
ps.gz 587 k,
pdf 247 k.

Home Page of
DOCUMENTA MATHEMATICA