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Titlebook: Conjectures in Arithmetic Algebraic Geometry; A Survey Wilfred W. J. Hulsbergen Book 1992 Springer Fachmedien Wiesbaden 1992 Algebra.Arithm

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The Explanation of Flow Systems,for Beilinson’s conjectures. These conjectures are then formulated in such a way that they generalize, at the same time, a conjecture of Deligne on the values of L-functions of motives at so-called critical points. We will state the conjectures only for smooth projective varieties defined over the r
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The Explanation of Network Form,rd conjecture regards this situation for smooth, projective varieties over ., and reduces to a weakened form of the Birch & Swinnerton-Dyer Conjectures in the case of an elliptic curve or an abelian variety over .. The elliptic regulator is generalized to become the determinant of an arithmetic inte
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Transport for the Space Economyight 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
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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.
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