Kay Rülling (Universität Wuppertal)

Abstract: The theory of cube invariant modulus sheaves developed by Kahn-Miyazaki-Saito-Yamazaki allows to define for any sheaf with transfers and any smooth k-scheme X with effective Cartier divisor D a sheaf whose sections over X can be interpreted as regular sections on the complement of D with pole order at infinity bounded by D. This construction is functorial and has a certain universal property, which makes it hard to compute explicitly. We apply it to the de Rham-Witt sheaves in positive characteristic p and show that in case the support of D has simple normal crossings these sheaves correspond under Grothendieck duality to de Rham Witt sheaves with zeros along D. From this we deduce refined versions of Ekedahl duality, Poincaré duality for crystalline cohomology, and Milne duality for motivic cohomology with p-primary torsion coefficients. This is joint work with Fei Ren.

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