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Abstract: We study the construction and properties of the Gysin triangle in anaxiomatic framework which covers triangulated mixed motives and MGl-modulesover an arbitrary base S. This allows to define the Gysin morphism associatedto a projective morphism between smooth S-schemes and prove duality forprojective smooth S-schemes. As part of the construction, cobordism classes areconsidered and we give a proof of the Myschenko theorem generalized in ourcontext - this in fact gives another proof of the latter theorem in classicalstable homotopy through complex realization. Finally, these constructions applyto rigid cohomology through the notion of a mixed Weil theory introduced byD.-C. Cisinski and the author in another work.



Author: F. Déglise

Source: https://arxiv.org/







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