Hermitian K-theory for stable ∞-categories III: Grothendieck-Witt groups of rings
with Emanuele Dotto, Yonatan Harpaz, Fabian Hebestreit, Markus Land, Kristian Moi, Denis Nardin, Thomas Nikolaus and Wolfgang Steimle
1st appeared online on the 16-09-2020
MSC 2010: 11E70, 18F25, 19G38 (Primary), 11E39, 11E81, 19D25 (Secondary)This is the third article in a series on the hermitian K-theory of stable ∞-categories with quadratic functors. The first, with the basic formalism, is here: Foundations. The second, with the definition and study of the Grothendieck-Witt groups is here: Cobordism categories and additivity.
In this third article, we apply the framework previously developed to study concrete problems on the hermitian K-theory of rings. We compute the Grothendieck-Witt groups of symmetric forms of integers (up to 20 000 unconditionally and otherwise under Vandiver's conjecture about K-theory) and we solve Thomason's homotopy limit problem for Dedekind rings with a number field as fraction field.
