Refines cohomology of the structure sheaf to an A¹-invariant theory with O_K-lattice values for smooth schemes over non-archimedean fields using tame cohomology and rigid analytic geometry.
A construction of tame sheaves and tame de Rham--Witt cohomology
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abstract
In this article, we consider an algebraic version of the tame site of a pair $(X,\widetilde{X})$. With this definition, we provide a general machinery to construct a tame sheaf from the data of an \'etale sheaf on $X$ and a family of local tame sections. We apply this construction to the big de Rham--Witt sheaves with tame sections defined by log poles and, over a field, to reciprocity sheaves, and deduce some consequences. As an application, we compare tame syntomic cohomology with the Nygaard filtration on the tame de Rham--Witt complex.
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math.AG 1years
2026 1verdicts
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Birational and $\mathbf{A}^1$-invariant lattices in the cohomology of the structure sheaf over non-archimedean fields
Refines cohomology of the structure sheaf to an A¹-invariant theory with O_K-lattice values for smooth schemes over non-archimedean fields using tame cohomology and rigid analytic geometry.