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On the Chow Groups of Supersingular Varieties
Canadian Mathematical Bulletin, 2002AbstractWe compute the rational Chow groups of supersingular abelian varieties and some other related varieties, such as supersingular Fermat varieties and supersingular K3 surfaces. These computations are concordant with the conjectural relationship, for a smooth projective variety, between the structure of Chow groups and the coniveau filtration on ...
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NORI’S CONNECTIVITY THEOREM AND HIGHER CHOW GROUPS
Journal of the Institute of Mathematics of Jussieu, 2002Let \(X\) be a smooth complex projective variety of dimension \(n+r\), and let \(L_1, \ldots, L_r\) be ample line bundles on \(X\). If \(B= \sum_i H^0 (X,L_i)\), then the connectivity theorem of \textit{M. V. Nori} [Invent. Math. 111, 349--373 (1993; Zbl 0822.14008)] compares the cohomology of \(X\times B\) and \(Y_B\), where \(Y_B\) is a locally ...
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Regulators on Higher Chow Groups
2018There are two natural questions one can ask about the higher Chow group of number fields: One is its torsion, the other one is its relation with the homology of GLn. For the first question, based on some earlier work, the integral regulator on higher Chow complexes introduced here can put a lot of earlier result on a firm ground.
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Chow group of 1-cycles of the moduli of parabolic bundles over a curve
Proceedings of the Indian Academy of Sciences: Mathematical Sciences, 2021Sujoy Chakraborty
exaly