The paper constructs a new category of Nisnevich sheaves with transfers on non-proper modulus pairs, proves it is a Grothendieck abelian category, and computes its Ext groups as filtered colimits of Nisnevich cohomology.
Reciprocity sheaves, II
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We exhibit an intimate relationship between "reciprocity sheaves" from arXiv:1402.4201 [math.AG] and "modulus sheaves with transfers" from arXiv:1908.02975 [math.AG] and arXiv:1910.14534 [math.AG].
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Motives with modulus, I: Modulus sheaves with transfers for non-proper modulus pairs
The paper constructs a new category of Nisnevich sheaves with transfers on non-proper modulus pairs, proves it is a Grothendieck abelian category, and computes its Ext groups as filtered colimits of Nisnevich cohomology.