New York Journal of Mathematics
Volume 28 (2022), 824-834


Junnosuke Koizumi

Zeroth A1-homology of smooth proper varieties

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Published: June 6, 2022.
Keywords: motivic homotopy theory.
Subject: Primary 14F42; Secondary 14E99.

We give an explicit formula for the zeroth A1-homology sheaf of a smooth proper variety. We also provide a simple proof of a theorem of Kahn-Sujatha which describes hom sets in the birational localization of the category of smooth varieties.


I am grateful to Shuji Saito for supporting me to learn A1-homotopy theory. I would like to thank Bruno Kahn for pointing out the necessity of a restriction on DVRs. I would like to thank Aravind Asok for helpful comments on the A1-locality of classifying spaces. I would also like to thank Anand Sawant and Amit Hogadi for encouraging me to write up the paper. Finally, I would like to thank the referee for many helpful comments.

Author information

Junnosuke Koizumi:
Graduate School of Mathematical Sciences
University of Tokyo
3-8-1 Komaba, Meguro-ku, Tokyo 153-8914, Japan