Numerical verification of Beilinson’s conjecture for K2 of hyperelliptic curves
نویسندگان
چکیده
We construct families of hyperelliptic curves over Q of arbitrary genus g with (at least) g integral elements in K2. We also verify the Beilinson conjectures about K2 numerically for several curves with g = 2, 3, 4 and 5. The first few sections of the paper also provide an elementary introduction to the Beilinson conjectures for K2 of curves.
منابع مشابه
Beilinson’s Tate conjecture for K2 and finiteness of torsion zero-cycles on elliptic surface
2 Preliminaries 4 2.1 Syntomic cohomology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.2 Syntomic cohomology with log poles . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.3 Symbol maps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.4 Tate curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.5...
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