Abstract
In this chapter we consider smooth projective varieties defined over Q and we define their L-functions. The whole formalism depends on several conjectures, suggested by the zero- and one-dimensional cases. The main ingredient of this chapter, Deligne-Beilinson cohomology, is introduced and shown to be a Poincaré duality theory. Such a (co)homology theory has the right properties to admit a formalism of characteristic classes which will generalize the classical regulator. This will be further explained in the next chapter.
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© 1992 Friedr. Vieweg & Sohn Verlagsgesellschaft mbH, Braunschweig/Wiesbaden
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Hulsbergen, W.W.J. (1992). The general formalism of L-functions, Deligne cohomology and Poincaré duality theories. In: Conjectures in Arithmetic Algebraic Geometry. Aspects of Mathematics, vol 18. Vieweg+Teubner Verlag, Wiesbaden. https://doi.org/10.1007/978-3-322-85466-7_4
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DOI: https://doi.org/10.1007/978-3-322-85466-7_4
Publisher Name: Vieweg+Teubner Verlag, Wiesbaden
Print ISBN: 978-3-528-06433-4
Online ISBN: 978-3-322-85466-7
eBook Packages: Springer Book Archive