The kinfolk that may or may still exist among algebraic cycles, algebraic K-theory, and the cohomology of - probably singular - forms, are the subject of research of this publication. the writer proceeds in an axiomatic means, combining the options of twisted Poincaré duality theories, weights, and tensor different types. One hence arrives at generalizations to arbitrary different types of the Hodge and Tate conjectures to particular conjectures on l-adic Chern characters for worldwide fields and to sure counterexamples for extra basic fields. it truly is to be was hoping that those kinfolk ions will in the end be defined via an appropriate tensor type of combined reasons. An approximation to this is often built within the atmosphere of absolute Hodge cycles, via extending this idea to arbitrary forms. The booklet can serve either as a advisor for the researcher, and as an creation to those rules for the non-expert, supplied (s)he is aware or is keen to profit approximately K-theory and the normal cohomology theories of algebraic types.
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