The Wu relations in real algebraic geometry
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866929742008025088 |
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| author | Benoist, Olivier Wittenberg, Olivier |
| author_facet | Benoist, Olivier Wittenberg, Olivier |
| contents | We construct and study relations between Chern classes and Galois cohomology classes in the Gal(C/R)-equivariant cohomology of real algebraic varieties with no real points. We give applications to the topology of their sets of complex points, and to sums of squares problems. In particular, we show that -1 is a sum of 2 squares in the function field of any smooth projective real algebraic surface with no real points and with vanishing geometric genus, as well as higher-dimensional generalizations of this result. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_11603 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Wu relations in real algebraic geometry Benoist, Olivier Wittenberg, Olivier Algebraic Geometry Algebraic Topology 14P25, 57R20, 55S10, 11E25 We construct and study relations between Chern classes and Galois cohomology classes in the Gal(C/R)-equivariant cohomology of real algebraic varieties with no real points. We give applications to the topology of their sets of complex points, and to sums of squares problems. In particular, we show that -1 is a sum of 2 squares in the function field of any smooth projective real algebraic surface with no real points and with vanishing geometric genus, as well as higher-dimensional generalizations of this result. |
| title | The Wu relations in real algebraic geometry |
| topic | Algebraic Geometry Algebraic Topology 14P25, 57R20, 55S10, 11E25 |
| url | https://arxiv.org/abs/2405.11603 |