{
  "abstract": "In [8], a non-Archimedean analogue of the space of translation-invariant even valuations on convex sets was introduced. In [7], motivated by a further analogy with the classical theory, this space was equipped with two multiplicative structures, the product and the convolution. Both structures satisfy Poincare duality and the (non-mixed) hard Lefschetz theorem. In this paper, we formulate a conjecture concerning a more general mixed versions of the hard Lefschetz theorem and the Hodge-Riemann relations. We prove the non-mixed Hodge-Riemann relations in degree 1 for the product and, equivalently, in codegree 1 for the convolution.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.25641",
  "author_total": 1,
  "authors": [
    {
      "name": "Semyon Alesker"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/c7m0y51zq32br.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.25641",
  "fulltext_url": null,
  "id": "c7m0y51zq32br",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.25641",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.MG"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7165910941",
  "pdf_url": "https://arxiv.org/pdf/2606.25641",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/c7m0y51zq32br.ris",
  "sources": [
    {
      "first_seen": "2026-11-05T15:21:00Z",
      "native_id": "2606.25641",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.25641"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.MG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Towards Hodge-Riemann relations for non-Archimedean analogs of valuations on convex sets",
  "title_text": "Towards Hodge-Riemann relations for non-Archimedean analogs of valuations on convex sets",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:25Z",
  "url": "https://research.draconitic.com/paper/c7m0y51zq32br",
  "venue": "arXiv",
  "versions": []
}