Vasudevan Srinivas (Tata Institute)

In this talk, I'll survey some recent results on zero cycles on singular

varieties. After reviewing the relevant definitions, and giving some

background, I'll discuss (i) a Roitman theorem for torsion 0-cycles for

complex projective varieties (joint work with J. Biswas) (ii) the

construction of a generalized Albanese variety for a projective variety

with arbitrary singularities (joint work with H. Esnault and E. Viehweg),

and (iii) a formula, conjectured earlier, which describes the Chow group

of zero cycles of a normal quasi-projective surface X over a field, as an

inverse limit of relative Chow groups of a desingularisation Y relative

to multiples of the exceptional divisor (joint work with A. Krishna). We

also discuss some applications of this last result -- a relative version

of the famous Bloch Conjecture on 0-cycles, the triviality of the Chow

group of 0-cycles for any 2-dimensional normal graded Q-algebra

(analogue of the Bloch-Beilinson Conjecture), and the analogue of

the Roitman theorem for torsion 0-cycles in characteristic p>0 for

normal varieties (including the case of p-torsion).