Titlebook: Conjectures in Arithmetic Algebraic Geometry; A Survey Wilfred W. J. Hulsbergen Textbook 1994Latest edition Springer Fachmedien Wiesbaden 1

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Indecisive

Indelible

,The general formalism of ,-functions, Deligne cohomology and Poincaré duality theories,ures, suggested by the zero- and one-dimensional cases. The main ingredient of this chapter, Deligne-Beilinson cohomology, is introduced, and it can be shown to be a Poincaré duality theory in the sense of Bloch & Ogus. It even satisfies Gillet’s axioms for a generalized Riemann-Roch theorem for hig

谷物

Antecedent

,Beilinson’s second conjecture, m + 1. This leads to an old conjecture due to J. Tate and generalized by A. Beilinson. For Hilbert modular surfaces D. Ramakrishnan proved that part of motivic cohomology is enough to give a ?-structure on Deligne cohomology with volume (up to a non-zero rational number) equal to the first non-zero

Firefly

Firefly

Absolute Hodge cohomology, Hodge and Tate conjectures and Abel-Jacobi maps,ight filtration. In this way it applies to general schemes over the complex numbers. The relation with motivic cohomology is again given by a regulator map that is conjectured to have dense image, at least for smooth schemes that can be defined over a number field. This conjectured property induces

jocular

Mixed realizations, mixed motives and Hodge and Tate conjectures for singular varieties,ensions of their pure analogues and the corresponding categories should be tannakian. Deligne has suggested a somewhat different definition of mixed motives, but in both Jannsen’s and his conception the fundamental notion has become the realization.

Insatiable

Examples and Results,ant work of B. Gross and D. Zagier on the Birch & Swinnerton-Dyer Conjectures. Next, an overview of Deligne’s Conjecture on the L-function of an algebraic Hecke character is given. This conjecture is now a theorem, due to work of D. Blasius, G. Harder and N. Schappacher. The third and fourth section

Hallmark