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Abstract
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We construct and study a triangulated category of motives with modulus
over a field
that extends
Voevodsky’s category
in such a way as to encompass nonhomotopy invariant phenomena. In a similar way as
is constructed out
of smooth
-varieties,
is constructed out of
proper modulus pairs, introduced in Part I
of this work. To such a modulus pair we associate its motive in
. In some
cases, the
group in
between the motives of two modulus pairs can be described in terms of Bloch’s higher
Chow groups.
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Keywords
motives, modulus, reciprocity
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Mathematical Subject Classification
Primary: 19E15
Secondary: 14F42, 19D45, 19F15
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Milestones
Received: 22 February 2021
Revised: 23 July 2021
Accepted: 9 August 2021
Published: 20 June 2022
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