### Integral elements of K-theory and products of modular curves, by A J Scholl

In the first part of this paper we use de Jong's method of alterations
to contruct unconditionally the `integral' subspaces of motivic
cohomology (with rational coefficients) for Chow motives over local
and global fields - for the motive of a smooth and proper variety
possessing a regular model over the ring of integers of the base
field, this coincides with the image of the motivic cohomology of the
model in that of the generic fibre.

In the second part, we investigate the integrality of the elements
constructed by Beilinson in the motivic cohomology of the product of
two modular curves, completing the discussion in section 6 of his
paper `Higher regulators and values of L-functions' (J Soviet Math 30
(1985), 2036-2070).

This file uses the XY fonts.

Author's home page: http://fourier.dur.ac.uk:8000/~dma0ajs.

A J Scholl <a.j.scholl@durham.ac.uk>