Abstract
Let be a local ring in which 2 is invertible. It is known that the localization of the cohomology ring with respect to the class is isomorphic to the ring of continuous -valued functions on the real spectrum of . Let denote the powers of the fundamental ideal in the Witt ring of symmetric bilinear forms over . The starting point of this article is the “integral” version: the localization of the graded ring with respect to the class is isomorphic to the ring of continuous -valued functions on the real spectrum of .
This has interesting applications to schemes. For instance, for any algebraic variety over the field of real numbers and any integer strictly greater than the Krull dimension of , we obtain a bijection between the Zariski cohomology groups with coefficients in the sheaf associated to the -th power of the fundamental ideal in the Witt ring and the singular cohomology groups .
Citation
Jeremy Jacobson. "Real cohomology and the powers of the fundamental ideal in the Witt ring." Ann. K-Theory 2 (3) 357 - 385, 2017. https://doi.org/10.2140/akt.2017.2.357
Information