Zero-cycles on Singular Varieties

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).