On the $p$-primary and $p$-adic cases of the Isotropy Conjecture
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866911371277369344 |
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| author | Vishik, Alexander |
| author_facet | Vishik, Alexander |
| contents | The purpose of this note is to show that, in contrast to the ${\Bbb F}_p$-case (proven in [7]), the $p$-primary and $p$-adic cases of the Isotropy Conjecture, claiming that the isotropic Chow groups with ${\Bbb Z}/p^r$, $r>1$, respectively, with ${\Bbb Z}_p$-coefficients over a flexible field coincide with the numerical ones, don't hold. We show that the $BP$-theory with $I(\infty)$-primary, respectively, $I(\infty)$-adic coefficients may serve as a regular substitute for $p$-primary, respectively, $p$-adic Chow groups, which permits to extend the results of [6] to arbitrary primes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_07947 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the $p$-primary and $p$-adic cases of the Isotropy Conjecture Vishik, Alexander Algebraic Geometry 14C15, 14C25, 19E15 The purpose of this note is to show that, in contrast to the ${\Bbb F}_p$-case (proven in [7]), the $p$-primary and $p$-adic cases of the Isotropy Conjecture, claiming that the isotropic Chow groups with ${\Bbb Z}/p^r$, $r>1$, respectively, with ${\Bbb Z}_p$-coefficients over a flexible field coincide with the numerical ones, don't hold. We show that the $BP$-theory with $I(\infty)$-primary, respectively, $I(\infty)$-adic coefficients may serve as a regular substitute for $p$-primary, respectively, $p$-adic Chow groups, which permits to extend the results of [6] to arbitrary primes. |
| title | On the $p$-primary and $p$-adic cases of the Isotropy Conjecture |
| topic | Algebraic Geometry 14C15, 14C25, 19E15 |
| url | https://arxiv.org/abs/2601.07947 |