Kato's residue homomorphisms and reciprocity laws on arithmetic surfaces

Abstract

We explicitly study Kato's residue homomorphisms in Milnor $K$-theory, which are closely related to Contou-Carrère symbols. As applications we establish several reciprocity laws for certain locally defined maps on $K$-groups that are associated to arithmetic surfaces.

Substantially revised based a referee report

References in corpus (2)

• An explicit approach to residues on and dualizing sheaves of arithmetic surfaces
• On dlog image of K_2 of elliptic surface minus singular fibers

Cited by in corpus (1)

• Higher adeles and non-abelian Riemann-Roch