Higher Arithmetic $K$-Theory

Yuichiro Takeda

doi:10.2977/prims/1145475225

JournalsprimsVol. 41, No. 3pp. 599–681

Higher Arithmetic $K$ -Theory

Yuichiro Takeda
Kyushu University, Fukuoka, Japan

Download PDF

Abstract

A concrete deﬁnition of higher $K$ -theory in Arakelov geometry is given. The $K$ -theory deﬁned in this paper is a higher extension of the arithmetic $K_{0}$ -group of an arithmetic variety deﬁned by Gillet and Soulé. Products and direct images in this $K$ -theory are discussed.

Cite this article

Yuichiro Takeda, Higher Arithmetic $K$ -Theory. Publ. Res. Inst. Math. Sci. 41 (2005), no. 3, pp. 599–681

DOI 10.2977/PRIMS/1145475225