Bloch's conjecture revisited

Details Bloch's conjecture revisited Bloch's conjecture revisited

1995-03-16

arxiv.org/abs/alg-geom/9503008v1

C.R.Acad.Sci.Paris 321 (1995), 211-214

Mathematics

Algebraic Geometry

4 pages, LaTeX

Scientific paper

Let $X$ be a non-singular projective complex surface. We can show that Bloch's conjecture (i.e., that if $p_g=0$ then the Albanese kernel vanishes) is equivalent to the following statement: If $p_g(X)=0$ then for any given Zariski open $U\subset X$ and $\omega\in H^2(U,{\bf C})$ there is a smaller Zariski open $V\subset U$ such that $$\omega\mid_V =\omega'+\zeta$$ where $\omega'\in F^2H^2(V,{\bf C})$ and $\zeta$ is integral.

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