Higher K-theory of Algebraic Curves, by Masana Harada

[The paper has been withdrawn by the author, July 22, 2010.]

[The original paper, submitted Oct 14, 2008, revised Nov 24, 2008, has been revised March 10, 2009, with this comment:] This is an update to #915. The reasoning of 2.1.2 was not enough. Also the last corollary is corrected.

In this paper we construct a filtration on algebraic K-theory of a smooth projective curve over a field. The base field could be arbitrary, and the curve has to have some morphism onto the projective plane, which will exist after a finite extension of the base field. The quotients are filtered colimits of K-theory of Artinian algebras over the base field. These non-commutative algebras are associated to global geometry of the curve, and it is difficult to describe them in any explicit way. But we can get a vanishing result of K-theory with Q-coefficient of regular schemes over finite fields in degree above twice the dimension.

Masana Harada <harada@math.kyoto-u.ac.jp>