Real Regulators for Products of Elliptic Curves
Vol. 30 (2023), No. 3, Page 341–363.
Chen, Xi; Lewis, James D.
Real Regulators for Products of Elliptic Curves
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Abstract:
Assuming the Künneth decomposition of the Chow groups of products of very general Kummer surfaces, we prove that the Hodge-$\mathscr{D}$-conjecture fails for the real regulator $r_{k,1}$ on a product of $n$ very general elliptic curves for $2n\ge 3k-1\ge 8$.
Keywords: Higher Chow group, real regulator, algebraic cycle.
Mathematics Subject Classification (2020): Primary 14C25; Secondary 14F43, 14J28, 14K30.
Received: 2023-01-19
