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.
Ayoub, Motifs de vari\'et\'es analytiques rigides, M\'em
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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.