Euclidean quadratic forms and ADC forms II: integral forms
We study ADC quadratic forms and Euclidean quadratic forms over the integers, obtaining complete classification results in the positive case.
We study ADC quadratic forms and Euclidean quadratic forms over the integers, obtaining complete classification results in the positive case.
Existence of proper Gorenstein projective resolutions and Tate cohomology is proved over rings with a dualizing complex. The proofs are based on Bousfield Localization which is originally a method from algebraic topology.
An algebra homomorphism of the locatized affine rings of an algebraic variety is continuous in the Krull topology of the respective local rings. It is not necessarily open or closed in the Krull topology. However, we show that the induced map on the associated analytic local rings is also open and closed in the Krull topology. To do this we prove a conjecture of Tougeron which states that if is an analytic curve on an analytic variety and is a formal power series which is convergent when restricted...