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# 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

#### Author

#### Abstract

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.