Triangulated categories of relative 1-motives

2015/12/01 by Lehalleur, Simon Pepin · 1 citation
#14C15 (Primary) 14K30 #14F42 (Secondary) #14H40 #Algebraic Geometry (math.AG) #FOS: Mathematics #K-Theory and Homology (math.KT)

paper · doi:10.48550/arxiv.1512.00266

Abstract

We construct and study a candidate for the standard motivic t-structure on the triangulated category of relative cohomological 1-motives with rational coefficients over a noetherian finite dimensional scheme S. This t-structure is defined as a generated t-structure, and we show it is non-degenerate. We relate its heart MM¹(S) with Deligne 1-motives over S; in particular, when S is regular, the category of Deligne 1-motives embeds in MM¹(S) fully faithfully. We also study the inclusion of DA¹(S) into the larger category DA^coh(S) of relative cohomological motives on S, and prove that its right adjoint, the motivic Picard functor, preserves compact objects.

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• Deligne 1-motives with torsion and étale motives

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