Homology, Homotopy and Applications

Volume 13 (2011)

Number 2

Motives of some acyclic varieties

Pages: 329 – 335

DOI: https://dx.doi.org/10.4310/HHA.2011.v13.n2.a20


Aravind Asok (Department of Mathematics, University of Southern California, Los Angeles, Calif., U.S.A.)


We prove that the Voevodsky motive with $\mathbb{Z}$-coefficients (resp. $\mathbb{Q}$-coefficients) of a $\mathbb{Z}$-acylic (resp. $\mathbb{Q}$-acyclic) smooth complex variety of dimension $\leqslant 2$ is isomorphic to that of a point and discuss some related extensions.


$\mathbb{A}^1$-homotopy; motive

2010 Mathematics Subject Classification

14F42, 14R05, 19E15

Published 25 January 2012