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arXiv · 0712.1604

Around the Gysin triangle II

F. Déglise
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Abstract

We study the construction and properties of the Gysin triangle in an axiomatic framework which covers triangulated mixed motives and MGl-modules over an arbitrary base S. This allows to define the Gysin morphism associated to a projective morphism between smooth S-schemes and prove duality for projective smooth S-schemes. As part of the construction, cobordism classes are considered and we give a proof of the Myschenko theorem generalized in our context - this in fact gives another proof of the latter theorem in classical stable homotopy through complex realization. Finally, these constructions apply to rigid cohomology through the notion of a mixed Weil theory introduced by D.-C. Cisinski and the author in another work.

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F. Déglise. 2008-11-08. Around the Gysin triangle II. https://arxiv.org/abs/0712.1604

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