Papers › Weil-étale cohomology and duality for arithmetic schemes in negative weights
Weil-étale cohomology and duality for arithmetic schemes in negative weights
Alexey Beshenov
The archive published only this paper's code-link row. Authors, date and abstract are from arXiv's metadata (CC0), read from the Kaggle arXiv metadata snapshot of 2026-09-12 where its title matched the archive's; the title is the archive's.
Flach and Morin constructed in (Doc. Math. 23 (2018), 1425--1560) Weil-\'etale cohomology Hⁱ_(W,c) (X, ℤ (n)) for a proper, regular arithmetic scheme X (i.e. separated and of finite type over Spec ℤ) and n ∈ℤ. In the case when n < 0, we generalize their construction to an arbitrary arithmetic scheme X, thus removing the proper and regular assumption. The construction uses \'etale motivic cohomology groups Hⁱ(Xₑₜ, ℤᶜ(n)), as studied by Geisser (Ann. of Math. (2) 172 (2010), 1095--1126), and assumes their finite generation for n < 0. We give a class of X for which finite generation is known, and hence Hⁱ_(W,c) (X, ℤ (n)) is defined unconditionally.
Code
Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.
Code Syntology ran Syntology
Not run by Syntology. Nothing on this page verifies that the listed code works.
Results from the paper archive 2025-07-28
No leaderboard rows for this paper in the archive.
Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections