Adelic resolution for sheaves of $ K$-groups

Горчинский, Сергей Олегович

doi:10.1070/rm2007v062n01abeh004389

Cited by 1 publication

(5 citation statements)

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“…(Comparison with Gorchinskiy's theory) Statement and comparison maps in eq. 4.5 are entirely analogous to Gorchinskiy's comparison maps ν * [Gor07], [Gor08, Thm. 1.1 and map in Prop.…”

Section: Idèles With Cycle Module Coefficientsmentioning

confidence: 68%

“…1.5. See , , , , , for other adèle/idèle theories resolving particular types of sheaves under varying assumptions.…”

Section: Motivationmentioning

confidence: 99%

“…Given any such product, we obtain a graded-commutative product on the cycle cohomology groups well-defined product. Gorchinskiy constructed such a subcomplex in his theory of adically non-completed idèles [10] , [11].…”

Section: Remark 412mentioning

confidence: 99%

“…Osipov gave a theory for K ‐theory coefficients . Gorchinskiy developed a theory of “not adically completed idèles” with very general coefficients and in all dimensions , . A similar “adically uncompleted” theory for quasi‐coherent coefficients is due to Huber, again .…”

Section: Motivationmentioning

confidence: 99%

“…exhibits a well‐defined product. Gorchinskiy constructed such a subcomplex in his theory of adically non‐completed idèles , .…”

Section: Idèles With Cycle Module Coefficientsmentioning

confidence: 99%

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Geometric two‐dimensional idèles with cycle module coefficients

Braunling

2014

Mathematische Nachrichten

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We give a theory of idèles with coefficients for smooth surfaces over a field. It is an analogue of Beilinson/Huber's theory of higher adèles, but handling cycle module sheaves instead of quasi-coherent ones. We prove that they give a flasque resolution of the cycle module sheaves in the Zariski topology. As a technical ingredient we show the Gersten property for cycle modules on equicharacteristic complete regular local rings, which might be of independent interest.

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“…(Comparison with Gorchinskiy's theory) Statement and comparison maps in eq. 4.5 are entirely analogous to Gorchinskiy's comparison maps ν * [Gor07], [Gor08, Thm. 1.1 and map in Prop.…”

Section: Idèles With Cycle Module Coefficientsmentioning

confidence: 68%

“…1.5. See , , , , , for other adèle/idèle theories resolving particular types of sheaves under varying assumptions.…”

Section: Motivationmentioning

confidence: 99%