Frobenius structure and $p$-adic zeta values
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866914041781288960 |
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| author | Beukers, Frits Vlasenko, Masha |
| author_facet | Beukers, Frits Vlasenko, Masha |
| contents | For differential operators of Calabi-Yau type, Candelas, de la Ossa and van Straten conjecture the appearance of $p$-adic zeta values in the matrix entries of their $p$-adic Frobenius structure expressed in the standard basis of solutions near a MUM-point. We prove that this phenomenon holds for simplicial and hyperoctahedral families of Calabi-Yau hypersurfaces in $n$ dimensions, in which case the Frobenius matrix entries are rational linear combinations of products of $ζ_p(k)$ with $1 < k < n$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_09603 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Frobenius structure and $p$-adic zeta values Beukers, Frits Vlasenko, Masha Number Theory Mathematical Physics Algebraic Geometry For differential operators of Calabi-Yau type, Candelas, de la Ossa and van Straten conjecture the appearance of $p$-adic zeta values in the matrix entries of their $p$-adic Frobenius structure expressed in the standard basis of solutions near a MUM-point. We prove that this phenomenon holds for simplicial and hyperoctahedral families of Calabi-Yau hypersurfaces in $n$ dimensions, in which case the Frobenius matrix entries are rational linear combinations of products of $ζ_p(k)$ with $1 < k < n$. |
| title | Frobenius structure and $p$-adic zeta values |
| topic | Number Theory Mathematical Physics Algebraic Geometry |
| url | https://arxiv.org/abs/2302.09603 |