# Higher semiadditive Grothendieck-Witt theory and the $K(1)$-local sphere

@inproceedings{Carmeli2021HigherSG, title={Higher semiadditive Grothendieck-Witt theory and the \$K(1)\$-local sphere}, author={Shachar Carmeli and Allen Yuan}, year={2021} }

We develop a higher semiadditive version of Grothendieck-Witt theory. We then apply the theory in the case of a finite field to study the higher semiadditive structure of the K(1)local sphere at the prime 2. As a further application, we compute and clarify certain power operations in the homotopy of the K(1)-local sphere.

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