Etale motivic cohomology and algebraic cycles
-- V. Srinivas, April 3, 2015

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This talk will report on joint work with A. Rosenschon. There
are examples (which I'll briefly discuss) showing that the
torsion and co-torsion of Chow groups are complicated, in
general, except in the "classical" cases (divisors and
0-cycles, and torsion in codimension 2); also the integral
Hodge conjecture is known to fail. Instead, we may (following
Lichtenbaum) consider the etale Chow groups, which coincide
with the usual ones if we use rational coefficients; we show
that they have better "integral" properties if we work over
the complex numbers (eg the integral Hodge conjecture for these
is equivalent to the usual rational Hodge Conjecture). In
contrast, they can have infinite torsion in some arithmetic
situations (the usual Chow groups are conjectured to be
finitely generated).