Weil restriction, cellular structures and Milnor-Witt K-theory

The category of strictly $\mathbb{A}^1$-invariant sheaves is central to the development of $\mathbb{A}^1$-algebraic topology over a field. It is a nontrivial fact that this is an abelian, symmetric monoidal category. I will outline a fundamental computation in this category, namely that of the tensor product of the Milnor-Witt K-theory sheaf with the so-called free strictly $\mathbb{A}^1$-invariant sheaf on a point, defined over a finite separable field extension of the base field. The computation is made possible by the use of cellular $\mathbb{A}^1$-homology. If time permits, I will discuss a few applications of our main results.

This talk is based on joint work with Fabien Morel.

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