A Nisnevich Local Bloch-Ogus Theorem over a General Base

A Bloch-Ogus Theorem for henselian local rings in mixed characteristic

We show a conditional exactness statement for the Nisnevich Gersten complex associated to an $\mathbb{A}^1$-invariant cohomology theory with Nisnevich descent for smooth schemes over a Dedekind ring with only infinite residue fields. As an application we derive a Nisnevich analogue of the Bloch-Ogus theorem for étale cohomology over a henselian discrete valuation ring with infinite residue field.

DVR 上的 Bloch-Ogus 定理

The Bloch-Ogus Theorem over DVR

本文证明了在离散赋值环上几何正则的正则局部环上的 Bloch-Ogus 定理，特别是混合特征下本质上光滑的正则局部环的情况。

Bloch-Ogus theorem,cyclic homology and deformation of Chow groups

Using Bloch-Ogus theorem and Chern character from K-theory to cyclic homology, we answer a question of Green and Griffiths on extending Bloch formula. Moreover, we construct a map from local Hilbert functor to local cohomology. With suitable assumptions, we use this map to answer a question of Bloch on constructing a natural transformation from local Hilbert functor to cohomological Chow groups.

Invariants birationnels dans la suite spectrale de Bloch-Ogus

For a field k of cohomological dimension d we prove that some E_2-terms of the Bloch-Ogus spectral sequence are birational invariants of smooth projective geometrically integral varieties over k. Over a finite field, we relate one of these invariants with the cokernel of the l-adic cycle class map for 1-cycles. Soit k un corps de dimension cohomologique d. On établit que certains E_2-termes de la suite spectrale de Bloch-Ogus sont des invariants birationnels des k-variétés projectives et lisses, géométriquement intègres. Sur un corps fini, on relie un de ces invariants au conoyau de l'applicat…

混合特征下光滑与半稳定概形的Bloch-Ogus理论

Bloch-Ogus theory for smooth and semi-stable schemes in mixed characteristic

本文研究了混合特征下光滑与半稳定概形上对偶同调理论的Bloch-Ogus理论与Gersten猜想，证明了光滑情形下的猜想及半稳定情形的特例，并由此导出优秀离散赋值环上局部环的Galois符号映射的满射性。

Germs of de Rham cohomology classes which vanish at the generic point

We show that hypergeometric differential equations, unitary and Gauss-Manin connections give rise to de Rham cohomology sheaves which do not admit a Bloch-Ogus resolution. The latter is in contrast to Panin's theorem asserting that corresponding étale cohomology sheaves do fulfill Bloch-Ogus theory.