5 papers
Weil restriction and the motivic cycle class map
Qi Ge, Guangzhao Zhu
We construct the Weil restriction map for l-adic cohomology and, more generally, for mixed Weil cohomology theories. We study its compatibility with the motivic cycle class map and…
Weil restriction, normal bundles and motivic Thom spaces
Guangzhao Zhu
Recent developments in motivic homotopy theory, particularly the construction of norm functors by Bachmann and Hoyois, have revealed deep connections between algebraic geometry and…
Rationality of cycles modulo 2 on products of generically smooth quadrics in characteristic 2
Stephen Scully, Guangzhao Zhu
A 2022 result of Karpenko establishes a conjecture of Hoffmann-Totaro on the possible values of the first higher isotropy index of an arbitrary anisotropic quadratic form of given…
Pullback and Weil transfer on Chow groups
Nikita Karpenko, Guangzhao Zhu
In the paper ``Weil transfer of algebraic cycles'', published by the second author in Indagationes Mathematicae about 25 years ago, a Weil transfer map for Chow groups of smooth al…
Artin shapes
Nikita Karpenko, Guangzhao Zhu
We introduce and study on examples a notion of the Artin shape for a motive related to a projective homogenous variety. We apply it to the problem of finding the complete motivic d…