Around the Gysin triangle I

TL;DR

This paper extends Gysin morphisms to arbitrary projective morphisms in mixed motives, proving classical formulas and applying the results to duality and motives with compact support.

Contribution

It introduces a new construction of Gysin morphisms for arbitrary projective morphisms in the setting of mixed motives, expanding previous results limited to closed immersions.

Findings

Established Gysin morphisms for all projective morphisms in mixed motives.

Proved classical formulas like projection and excess intersection formulas.

Applied the construction to duality and motives with compact support.

Abstract

We define and study Gysin morphisms on mixed motives over a perfect field. Our construction extends the case of closed immersions, already known from results of Voevodsky, to arbitrary projective morphisms. We prove several classical formulas in this context, such as the projection and excess intersection formulas, and some more original ones involving residues. Finally, we give an application of this construction to duality and motive with compact support.