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The Wu relations in real algebraic geometry
[Submitted on 19 May 2024 (v1), last revised 23 Jun 2026 (this v · 2026-06-25 · via math updates on arXiv.org

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Abstract: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.

Submission history

From: Olivier Benoist [view email]
[v1] Sun, 19 May 2024 16:18:43 UTC (68 KB)
[v2] Mon, 10 Jun 2024 14:42:44 UTC (69 KB)
[v3] Wed, 5 Mar 2025 09:02:15 UTC (71 KB)
[v4] Tue, 23 Jun 2026 19:01:12 UTC (79 KB)