Homology, Homotopy and Applications

Volume 3 (2001)

Number 2

Volume of a Workshop at Stanford University

Base change functors in the $\mathbb{A}^1$-stable homotopy category

Pages: 417 – 451

DOI: http://dx.doi.org/10.4310/HHA.2001.v3.n2.a8


Po Hu (Department of Mathematics, University of Chicago, Chicago, Illinois, U.S.A.)


We relate base change functors of sheaves in $\mathbb{A}^1$-homotopy theory to group change functors from equivariant homotopy theory, and use these functors to construct elements of the Picard group of the $\mathbb{A}^1$-stable homotopy category. We also prove an analogue of the Wirthmüller isomorphism from equivariant homotopy theory in the $\mathbb{A}^1$-context.


$A^1$-homotopy theory, Verdier duality, Wirthmüller isomorphism, Picard group

2010 Mathematics Subject Classification

Primary 14F05, 14F42. Secondary 55P91.

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