The polylogarithm motive over S = P^1 minus {0,1,∞} is realized as the relative cohomology motive of the complement of the hypersurface {1 - z t1⋯tn = 0} in A^n_S relative to the hyperplanes ti=0 and ti=1.
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Orlik–Solomon sheaf homology on a geometric lattice concentrates in top degree and decomposes as a sum of local OS algebras tensored with top homology of complementary geometric semilattices.
Computes étale Gm-cohomology of p-adic Stein spaces via principal units filtration, p-adic Hodge theory for U-cohomology, and Kummer sequences for Gm/U, with explicit formula applying to Drinfeld upper half space.
citing papers explorer
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A construction of the polylogarithm motive
The polylogarithm motive over S = P^1 minus {0,1,∞} is realized as the relative cohomology motive of the complement of the hypersurface {1 - z t1⋯tn = 0} in A^n_S relative to the hyperplanes ti=0 and ti=1.
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Orlik--Solomon sheaf homology of geometric lattices
Orlik–Solomon sheaf homology on a geometric lattice concentrates in top degree and decomposes as a sum of local OS algebras tensored with top homology of complementary geometric semilattices.
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$\mathbb{G}_m$-cohomology of $p$-adic Stein spaces
Computes étale Gm-cohomology of p-adic Stein spaces via principal units filtration, p-adic Hodge theory for U-cohomology, and Kummer sequences for Gm/U, with explicit formula applying to Drinfeld upper half space.