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Ramification theory for reciprocity sheaves, III, Abbes-Saito formula

We give a new geometric characterization of the motivic ramification filtration of reciprocity sheaves, by imitating a method used by Abbes and (Takeshi) Saito to study the ramification of torsors under finite étale groups. This new characterization is used to define characteristic forms for reciprocity sheaves. We obtain applications on pseudo-rational singularities and on questions regarding the representability of certain cohomology groups of reciprocity sheaves in the triangulated category of motives with modulus introduced by Kahn-Miyazaki-Saito-Yamazaki.

preprint2022arXivOpen access
Kay RüllingShuji Saito
math.AG
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Kay RüllingShuji Saito

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