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A Lefschetz (1,1) theorem for singular varieties | | Donu Arapura
; | | Date: |
2 May 2016 | | Abstract: | The goal of this article is to try understand where Hodge cycles on a
singular complex projective variety X come from. As a first step we consider
Hodge cycles on the maximal pure quotient $H^{2p}(X)/W_{2p-1}$, and introduce a
class of algebraic cycles that we call homologically Cartier, that should
conjecturally describe all such Hodge cycles. Secondly, given a singular
complex projective variety $X$, we show that there is a cycle map from motivic
cohomology group $H^{2p}_M(X,Q(p))$ to the space of weight 2p Hodge cycles in
$H^{2p}(X,Q)$. We conjecture that this is surjective when X is defined over the
algebraic closure of $mathbb{Q}$. We show that this holds integrally when p=1,
and we also give a concrete interpretation of motivic classes in this degree.
Finally, we show that the general conjecture holds for a self fibre product of
elliptic modular surfaces. | | Source: | arXiv, 1605.0587 | | Services: | Forum | Review | PDF | Favorites | |
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