Codimension 2 cycles of classifying spaces of low-dimensional algebraic tori

Nicole Lemire (University of Western Ontario)

15-Jul-2021, 16:00-17:00 (3 years ago)

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

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