Épijournal de Géométrie Algébrique· 2026Q1
Bloch-Ogus theory for smooth and semi-stable schemes in mixed characteristic
- 0citations
- Q1SCImago
- 2026year
Short summary
The Gersten conjecture is proven for étale cohomology with finite coefficients (coprime to residue characteristic) on smooth schemes in mixed characteristic, and a special case is shown for semi-stable schemes.
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Key points
- Proves the Gersten conjecture for étale cohomology with finite coefficients on smooth schemes in mixed characteristic.
- Establishes a special case of the Gersten conjecture for semi-stable schemes in mixed characteristic.
- Demonstrates the surjectivity of the Galois symbol map for local rings over excellent discrete valuation rings as a corollary.
- Applies to homology theories with duality, particularly étale cohomology with finite coefficients coprime to residue characteristic.
AI-generated from the title and abstract; the full text is not read.
Abstract
We study Bloch-Ogus theory and the Gersten conjecture for homology theories with duality satisfying certain properties, in particular for étale cohomology with finite coefficients coprime to the residue characteristic of the base, for smooth and semi-stable schemes in mixed characteristic. We prove the Gersten conjecture in the smooth case and prove a special case in the semi-stable situation. As a corollary of the smooth case, we obtain the surjectivity of the Galois symbol map for arbitrary local rings over an excellent discrete valuation ring.
The authors' abstract, as published at the source. Épijournal de Géométrie Algébrique, 2026 · DOI ↗
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Field: Geometry and Topology
Geometry and TopologyMathematics