{"id":"https://openalex.org/W7165910941","doi":"https://doi.org/10.48550/arxiv.2606.25641","title":"Towards Hodge-Riemann relations for non-Archimedean analogs of valuations on convex sets","display_name":"Towards Hodge-Riemann relations for non-Archimedean analogs of valuations on convex sets","publication_year":2026,"publication_date":"2026-06-24","ids":{"openalex":"https://openalex.org/W7165910941","doi":"https://doi.org/10.48550/arxiv.2606.25641"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2606.25641","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2606.25641","pdf_url":"https://arxiv.org/pdf/2606.25641","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2606.25641","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5015373986","display_name":"Semyon Alesker","orcid":"https://orcid.org/0000-0003-3856-9860","observed_orcids":["https://orcid.org/0000-0003-3856-9860"]},"institutions":[{"id":"https://openalex.org/I16391192","display_name":"Tel Aviv University","ror":"https://ror.org/04mhzgx49","country_code":"IL","type":"education","lineage":["https://openalex.org/I16391192"]}],"countries":["IL"],"is_corresponding":true,"raw_author_name":"Alesker, Semyon","raw_affiliation_strings":["Department of Mathematics , Tel Aviv University , Ramat Aviv 69978 Tel Aviv , Israel"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics , Tel Aviv University , Ramat Aviv 69978 Tel Aviv , Israel","institution_ids":["https://openalex.org/I16391192"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5015373986"],"corresponding_institution_ids":["https://openalex.org/I16391192"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.4066999852657318,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.4066999852657318,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.2953999936580658,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11830","display_name":"Point processes and geometric inequalities","score":0.1696999967098236,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/hodge-riemann-relations","display_name":"Hodge-Riemann relations","score":0.9269999861717224},{"id":"https://openalex.org/keywords/non-archimedean-valuations","display_name":"non-Archimedean valuations","score":0.8949999809265137},{"id":"https://openalex.org/keywords/translation-invariant-valuations","display_name":"translation invariant valuations","score":0.8500000238418579},{"id":"https://openalex.org/keywords/poincare-duality","display_name":"Poincar\u00e9 duality","score":0.8330000042915344},{"id":"https://openalex.org/keywords/hard-lefschetz-theorem","display_name":"Hard Lefschetz theorem","score":0.9470000267028809},{"id":"https://openalex.org/keywords/convex-geometry","display_name":"convex geometry","score":0.41499999165534973}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8222000002861023},{"id":"https://openalex.org/C42747912","wikidata":"https://www.wikidata.org/wiki/Q1048447","display_name":"Multiplicative function","level":2,"score":0.6728000044822693},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.6687999963760376},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.5705000162124634},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.5169000029563904},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.5159000158309937},{"id":"https://openalex.org/C2778023678","wikidata":"https://www.wikidata.org/wiki/Q554403","display_name":"Duality (order theory)","level":2,"score":0.44589999318122864},{"id":"https://openalex.org/C521332185","wikidata":"https://www.wikidata.org/wiki/Q185816","display_name":"Analogy","level":2,"score":0.43790000677108765},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.4350000023841858},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4235000014305115},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.39320001006126404},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3824000060558319},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.35740000009536743},{"id":"https://openalex.org/C123222754","wikidata":"https://www.wikidata.org/wiki/Q1070472","display_name":"Product topology","level":2,"score":0.33719998598098755},{"id":"https://openalex.org/C49870271","wikidata":"https://www.wikidata.org/wiki/Q193657","display_name":"Convex set","level":4,"score":0.3206000030040741},{"id":"https://openalex.org/C12108790","wikidata":"https://www.wikidata.org/wiki/Q2234833","display_name":"Convex analysis","level":4,"score":0.30489999055862427},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.2671000063419342},{"id":"https://openalex.org/C26390989","wikidata":"https://www.wikidata.org/wiki/Q2063099","display_name":"Poincar\u00e9 duality","level":3,"score":0.257099986076355},{"id":"https://openalex.org/C137212723","wikidata":"https://www.wikidata.org/wiki/Q1948412","display_name":"Morphism","level":2,"score":0.25589999556541443}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2606.25641","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2606.25641","pdf_url":"https://arxiv.org/pdf/2606.25641","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2606.25641","doi":"https://doi.org/10.48550/arxiv.2606.25641","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.25641","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2606.25641","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2606.25641","pdf_url":"https://arxiv.org/pdf/2606.25641","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7165910941.pdf","grobid_xml":"https://content.openalex.org/works/W7165910941.grobid-xml"},"referenced_works_count":1,"referenced_works":["https://openalex.org/W4390051099"],"related_works":["https://openalex.org/W4391013402","https://openalex.org/W4390051099","https://openalex.org/W4287592809","https://openalex.org/W3083065172","https://openalex.org/W2026730940","https://openalex.org/W195637059","https://openalex.org/W1593989707","https://openalex.org/W2091984925","https://openalex.org/W2563805612","https://openalex.org/W7096853424"],"abstract_inverted_index":{"In":[0,17,52],"[8],":[1],"a":[2,21,57,60],"non-Archimedean":[3],"analogue":[4],"of":[5,8,65],"the":[6,25,36,39,47,66,71,76,84,92],"space":[7,29],"translation-invariant":[9],"even":[10],"valuations":[11],"on":[12],"convex":[13],"sets":[14],"was":[15,30],"introduced.":[16],"[7],":[18],"motivated":[19],"by":[20],"further":[22],"analogy":[23],"with":[24,32],"classical":[26],"theory,":[27],"this":[28,53],"equipped":[31],"two":[33],"multiplicative":[34],"structures,":[35],"product":[37,85],"and":[38,46,70],"convolution.":[40,93],"Both":[41],"structures":[42],"satisfy":[43],"Poincare":[44],"duality":[45],"(non-mixed)":[48],"hard":[49,67],"Lefschetz":[50,68],"theorem.":[51],"paper,":[54],"we":[55],"formulate":[56],"conjecture":[58],"concerning":[59],"more":[61],"general":[62],"mixed":[63],"versions":[64],"theorem":[69],"Hodge-Riemann":[72,78],"relations.":[73],"We":[74],"prove":[75],"non-mixed":[77],"relations":[79],"in":[80,88],"degree":[81],"1":[82,90],"for":[83,91],"and,":[86],"equivalently,":[87],"codegree":[89]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-06-26T00:00:00"}
