Weight filtration on the cohomology of algebraic varieties
| dc.creator | Hanamura, Masaki | |
| dc.creator | Saito, Morihiko | |
| dc.date | 2006-05-23 | |
| dc.date | 2006-06-16 | |
| dc.date.accessioned | 2026-07-07T07:14:28Z | |
| dc.date.available | 2026-07-07T07:14:28Z | |
| dc.description | We show that the etale cohomology (with compact supports) of an algebraic variety $X$ over an algebraically closed field has the canonical weight filtration $W$, and prove that the middle weight part of the cohomology with compact supports of $X$ is a subspace of the intersection cohomology of a compactification $X'$ of X, or equivalently, the middle weight part of the (so-called) Borel-Moore homology of $X$ is a quotient of the intersection cohomology of $X'$. We are informed that this has been shown by A. Weber in the case $X$ is proper (and $k=\bC$) using a theorem of G. Barthel, J.-P. Brasselet, K.-H. Fieseler, O. Gabber and L. Kaup on morphisms between intersection complexes. We show that the assertion immediately follows from Gabber's purity theorem for intersection complexes. | |
| dc.description | 11 pages, title is changed | |
| dc.identifier | https://arxiv.org/abs/math/0605603 | |
| dc.identifier | http://arxiv.org/abs/math/0605603 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/112885 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 14F43 | |
| dc.title | Weight filtration on the cohomology of algebraic varieties | |
| dc.type | text |