an:04204522
Zbl 0729.14002
Deninger, Christopher; Scholl, Anthony J.
The Beilinson conjectures
EN
L-functions and arithmetic, Proc. Symp., Durham/UK 1989, Lond. Math. Soc. Lect. Note Ser. 153, 173-209 (1991).
1991
a
14A10 14C35 14G10 14C25
Beilinson conjectures; generalized regulators; Beilinson's motivic cohomology; higher Chow groups; generalized cycle maps; Eisenstein symbol; mixed motives; Deligne conjecture
[For the entire collection see Zbl 0718.00005.]
The Beilinson conjectures describe the leading coefficients of L-series of varieties over number fields up to rational factors in terms of generalized regulators. The authors follow \textit{S. Bloch} [in Algebraic Geometry, Proc. Lefschetz Centen. Conf., Mexico/City 1984, part I, Contemp. Math. 58, 65-79 (1986; Zbl 0605.14017)] rather closely to describe Beilinson's motivic cohomology and regulator map in terms of higher Chow groups and generalized cycle maps, and then sketch how much of the known evidence in favour of these conjectures can be obtained in a uniform way. The basic construction is Beilinson's Eisenstein symbol.
In an appendix the authors construct a map from higher Chow theory to a suitable Ext-group in the category of mixed motives. This smoothes the way towards an interpretation of Beilinson's conjectures in terms of the Deligne conjecture for critical mixed motives.
Li Fuan (Beijing)
Zbl 0718.00005; Zbl 0605.14017