RECIPROCITY SHEAVES AND THEIR RAMIFICATION FILTRATIONS

Abstract We define a motivic conductor for any presheaf with transfers F using the categorical framework developed theory of motives modulus by Kahn, Miyazaki, Saito and Yamazaki. If is reciprocity sheaf, this yields an increasing exhaustive filtration on $F(L)$ , where L henselian discrete valuation field geometric type over perfect ground field. show that if smooth group scheme, then extends Rosenlicht–Serre conductor; assigns to X finite characters abelianised étale fundamental agrees Artin defined Kato Matsuda; integrable rank $1$ connections (in characteristic $0$ ), it irregularity. also machinery gives rise torsors under flat schemes base field, which we believe be new. introduce general notion conductors presheaves minimal only fields residue can uniquely extended all such without restriction For example, Kato–Matsuda characterised as canonical extension classical in case