The period-index conjecture for abelian threefolds and Donaldson-Thomas theory
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866910478875230208 |
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| author | Hotchkiss, James Perry, Alexander |
| author_facet | Hotchkiss, James Perry, Alexander |
| contents | We prove the period-index conjecture for unramified Brauer classes on abelian threefolds. To do so, we develop a theory of reduced Donaldson-Thomas invariants for 3-dimensional Calabi-Yau categories, with the feature that the noncommutative variational integral Hodge conjecture holds for classes with nonvanishing invariant. The period-index result is then proved by interpreting it as the algebraicity of a Hodge class on the twisted derived category, and specializing within the Hodge locus to an untwisted abelian threefold with nonvanishing invariant. As a consequence, we also deduce the integral Hodge conjecture for generically twisted abelian threefolds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_03315 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The period-index conjecture for abelian threefolds and Donaldson-Thomas theory Hotchkiss, James Perry, Alexander Algebraic Geometry We prove the period-index conjecture for unramified Brauer classes on abelian threefolds. To do so, we develop a theory of reduced Donaldson-Thomas invariants for 3-dimensional Calabi-Yau categories, with the feature that the noncommutative variational integral Hodge conjecture holds for classes with nonvanishing invariant. The period-index result is then proved by interpreting it as the algebraicity of a Hodge class on the twisted derived category, and specializing within the Hodge locus to an untwisted abelian threefold with nonvanishing invariant. As a consequence, we also deduce the integral Hodge conjecture for generically twisted abelian threefolds. |
| title | The period-index conjecture for abelian threefolds and Donaldson-Thomas theory |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2405.03315 |