Around the Gysin triangle II

Details Around the Gysin triangle II Around the Gysin triangle II

2007-12-10

arxiv.org/abs/0712.1604v2

Mathematics

Algebraic Geometry

The major change is a correction of the formula involving multiplicities with a correction term due to the formal group law (i

Scientific paper

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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