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).

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