Steenrod operations and algebraic classes
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866929751852056576 |
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| author | Benoist, Olivier |
| author_facet | Benoist, Olivier |
| contents | Based on a relative Wu theorem in étale cohomology, we study the compatibility of Steenrod operations on Chow groups and on étale cohomology. Using the resulting obstructions to algebraicity, we construct new examples of non-algebraic cohomology classes over various fields ($\mathbb{C}$, $\mathbb{R}$, $\overline{\mathbb{F}}_p$, $\mathbb{F}_q$).
We also use Steenrod operations to study the mod $2$ cohomology classes of a compact $\mathcal{C}^{\infty}$ manifold $M$ that are algebraizable, i.e. algebraic on some real algebraic model of $M$. We give new examples of algebraizable and non-algebraizable classes, answering questions of Benedetti, Dedò and Kucharz. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2209_03685 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Steenrod operations and algebraic classes Benoist, Olivier Algebraic Geometry 14C25, 55S10, 14G15, 14P05 Based on a relative Wu theorem in étale cohomology, we study the compatibility of Steenrod operations on Chow groups and on étale cohomology. Using the resulting obstructions to algebraicity, we construct new examples of non-algebraic cohomology classes over various fields ($\mathbb{C}$, $\mathbb{R}$, $\overline{\mathbb{F}}_p$, $\mathbb{F}_q$). We also use Steenrod operations to study the mod $2$ cohomology classes of a compact $\mathcal{C}^{\infty}$ manifold $M$ that are algebraizable, i.e. algebraic on some real algebraic model of $M$. We give new examples of algebraizable and non-algebraizable classes, answering questions of Benedetti, Dedò and Kucharz. |
| title | Steenrod operations and algebraic classes |
| topic | Algebraic Geometry 14C25, 55S10, 14G15, 14P05 |
| url | https://arxiv.org/abs/2209.03685 |