Codimension 2 cycles of classifying spaces of low-dimensional algebraic tori
Nicole Lemire (University of Western Ontario)
Abstract: Let T be an algebraic torus over a field F, and let CH^2(BT) be the Chow group of codimension 2 cycles in its classifying space. Following work of Blinstein and Merkurjev on the structure of the torsion part of CH^2(BT), Scavia, in a recent preprint, found an example of an algebraic torus with non-trivial torsion in CH^2(BT). In joint work with Alexander Neshitov, we show computationally that the group CH^2(BT) is torsion-free for all algebraic tori of dimension at most 5 and determine the conjugacy classes of finite subgroups of GL_6(Z) which correspond to 6-dimensional tori with nontrivial torsion in CH^2(BT). Some interesting properties of the structure of low-dimensional algebraic tori are involved.
algebraic geometry
Audience: researchers in the topic
ZAG (Zoom Algebraic Geometry) seminar
Series comments: Description: ZAG seminar
The seminar takes place on Tuesdays and Thursdays via Zoom. Zoom passwords are given via mailing list on Fridays. To join the mailing list go to the website.
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Organizers: | Jesus Martinez Garcia*, Ivan Cheltsov*, Jungkai Chen, Jérémy Blanc, Ernesto Lupercio, Yuji Odaka, Zsolt Patakfalvi, Julius Ross, Cristiano Spotti, Chenyang Xu |
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