Duality in the Étale Cohomology of One-Dimensional Proper Schemes and Generalizations.
In this article we give an introduction to mixed motives and sketch a couple of ways to construct examples.
We construct a two dimensional foliation with dense leaves on the Heisenberg nilmanifold for which smooth leafwise Hodge decomposition does not hold. It is also shown that a certain type of dynamical trace formulas relating periodic orbits with traces on leafwise cohomologies does not hold for arbitrary flows.
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