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Abstract
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Using the theory of framed correspondences developed by Voevodsky and the
machinery of framed motives introduced and developed in recent work of Garkusha
and Panin, various explicit fibrant resolutions for a motivic Thom spectrum
are
constructed in this paper. The bispectrum
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each term of which is a twisted
-framed motive of
, is introduced and
shown to represent
in the category of bispectra. As a topological application, it is proved that the
-framed motive with
finite coefficients
,
, of the point
evaluated at
is a quasifibrant model of
the topological
-spectrum
whenever the
base field
is algebraically closed of characteristic zero with an embedding
.
Furthermore, the algebraic cobordism spectrum
is computed in terms
of
-correspondences.
It is also proved that
is represented by a bispectrum each term of which is a sequential colimit of simplicial
smooth quasiprojective varieties.
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Keywords
motivic homotopy theory, motivic Thom spectra, $E$-framed
motives
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Mathematical Subject Classification
Primary: 14F42, 55P42
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Milestones
Received: 18 October 2022
Revised: 18 June 2023
Accepted: 3 August 2023
Published: 27 August 2023
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