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

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.

Keywords

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

2010 Mathematics Subject Classification

Primary 14F05, 14F42. Secondary 55P91.

Full Text (PDF format)

Published 1 January 2001