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).