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Zero-Cycles And K-Theory On Normal Surfaces., Amalendu Krishna Dr.

Doctoral Theses

The main theme of this thesis is to study the theory of algebraic cycles on singular varieties over a field. This has been studied before extensively by Collins, Barbieri-Viale, Levine, Srinivas among several others. Our interest in this thesis is to address some well known problems in the theory of zero-cycles over nominal varieties. The use of K- theoretic techniques in our proofs illustrate the interplay between the study of algebraic cycles and algebraic K-theory.For a quasi-projective surface X over a field k, we define FA,(X) to be the subgroup of the Grothendieck group Ko(X) of vector bundies generated by …