Refined index obstructions for Brauer classes on an abelian variety
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866916046831616000 |
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| author | Mackall, Eoin |
| author_facet | Mackall, Eoin |
| contents | We produce refined index obstructions, generalizing recently constructed index obstructions due to de Jong and Perry, for topologically trivial Brauer classes on smooth and projective complex varieties. We show that our refined obstructions are more stringent than previous obstructions and, as a consequence, we produce more counterexamples to the integral Hodge conjecture. Throughout this work, we focus on algorithmic aspects of these obstructions and we illustrate many of these aspects through the concrete examples of complex abelian varieties. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_26407 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Refined index obstructions for Brauer classes on an abelian variety Mackall, Eoin Algebraic Geometry K-Theory and Homology Rings and Algebras 14F22, 14C30, 16K50 We produce refined index obstructions, generalizing recently constructed index obstructions due to de Jong and Perry, for topologically trivial Brauer classes on smooth and projective complex varieties. We show that our refined obstructions are more stringent than previous obstructions and, as a consequence, we produce more counterexamples to the integral Hodge conjecture. Throughout this work, we focus on algorithmic aspects of these obstructions and we illustrate many of these aspects through the concrete examples of complex abelian varieties. |
| title | Refined index obstructions for Brauer classes on an abelian variety |
| topic | Algebraic Geometry K-Theory and Homology Rings and Algebras 14F22, 14C30, 16K50 |
| url | https://arxiv.org/abs/2605.26407 |