A \(K\)-theoretic interpretation of real Deligne cohomology (Q2411343)

The author defines \(K\)-theory groups \(K_{\mathrm{Ban},>0}(A)\), for Fréchet algebras \(A\) and their pro-Banach completion. The main result of the paper is to compute \(K_{\mathrm{Ban},>0}(\mathcal{O}^{an}_X)\) for complex manifolds \(X\). As a result of these computations, the Author proves that \(K_{\mathrm{Ban},>0}(\mathcal{O}^{an}_X)\) is locally strictly quasi-isomorphic of the real Deligne complex, this also gives a new interpretation of Beilinson's regulator as a morphism between \(K\)-theories.