1. The arithmetic of Calabi-Yau motives and mobile higher regulators
- Author
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Golyshev, Vasily and Kerr, Matt
- Subjects
Mathematics - Algebraic Geometry ,11G40, 14C30, 14D07, 19F27 - Abstract
We construct elements in the motivic cohomology of certain rank 4 weight 3 Calabi-Yau motives, and write down explicit expressions for the regulators of these elements in the context of conjectures on $L$-values such as those of Beilinson or Bloch-Kato. We apply a combination of three ideas: (i) that a motive can be made to vary in a family in such a way that a desired motivic cohomology class is realized by relative cohomology; (ii) that there are ways to construct higher-rank (such as $2\times 2$) regulators from a single family; and (iii) that one can arrange elements in $H^4_{\text{Mot}}(X,\mathbb{Z}(p))$ with different $p$'s by choosing hypergeometric families with different local exponents., Comment: 39 pages; comments welcome!
- Published
- 2024