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We prove that exterior powers of (skew-)symmetric bundles induce a $lambda$-ring structure on the ring $GW^0(X) oplus GW^2(X)$, when $X$ is a scheme where $2$ is invertible. Using this structure, we define stable Adams operations on Hermitian $K$-theory. As a byproduct of our methods, we also compute the ternary laws associated to Hermitian $K$-theory.
This paper is the first in a series in which we offer a new framework for hermitian K-theory in the realm of stable $infty$-categories. Our perspective yields solutions to a variety of classical problems involving Grothendieck-Witt groups of rings an
We define Grothendieck-Witt spectra in the setting of Poincare $infty$-categories and show that they fit into an extension with a L- and an L-theoretic part. As consequences we deduce localisation sequences for Verdier quotients, and generalisations
We establish a fibre sequence relating the classical Grothendieck-Witt theory of a ring $R$ to the homotopy $mathrm{C}_2$-orbits of its K-theory and Ranickis original (non-periodic) symmetric L-theory. We use this fibre sequence to remove the assumpt
We provide a concrete introduction to the topologised, graded analogue of an algebraic structure known as a plethory, originally due to Tall and Wraith. Stacey and Whitehouse showed this structure is present on the cohomology operations for a suitabl
Recall that the definition of the $K$-theory of an object C (e.g., a ring or a space) has the following pattern. One first associates to the object C a category A_C that has a suitable structure (exact, Waldhausen, symmetric monoidal, ...). One then