On Hodge-Witt Sheaves with Modulus

par Atsushi Shiho (The University of Tokyo)

jeudi 18 juin 2026, 11:00 → 12:30 Europe/Paris

Amphithéâtre Léon Motchane (IHES)

Séminaire de géométrie arithmétique

Let k be a perfect field of characteristic p > 0. The Hodge-Witt sheaf is a sheaf with transfer on the category of smooth k-varieties. However, since it does not satisfy the cohomological A¹-invariance, the Hodge-Witt cohomology is not representable in Voevodsky's category of motives. One way to overcome this drawback is to consider the category of motives with modulus defined by Kahn-Miyazaki-Saito-Yamazaki. We define the Hodge-Witt sheaf for modulus pairs over k satisfying the properties called the cohomological cube invariance and the cohomological blow-up invariance. These imply that the Hodge-Witt cohomology is representable in the category of motives with modulus under resolution of singularities. Also, we try to discuss properties of our Hodge-Witt sheaves for modulus pairs and possible relationship with another construction by Ren-Rulling. This is partly joint work in progress with Veronika Ertl. 

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