Washnitzer’s conjecture and the cohomology of a variety with a single isolated singularity.

Let X be an irreducible quasiprojective variety over C, and consider its singular cohomology H(X;C). The map :X to Xalg of sites relates the sheaf cohomology in the Zariski (algebraic) topology to the singular cohomology via the Leray spectral sequence ...., which in turn provides a filtration onH(X,C).Washnitzer conjectured for nonsingular X that the filtration is the arithmetic filtration, where NpH(X,C) consists of classes which vanish when restricted to the complement of some subvariety of codimension p, and the conjecture was proved in a paper by S. Bloch and A. Ogus In this paper, the author proves the conjecture for varieties X with a single singular point. The method is to construct an arithmetic spectral sequence with same abutment and providing the desired filtration, and then to show it agrees with the Leray spectral sequence.