Algebraic Geometry最新文献_第5页

A functorial approach to regular homomorphisms 正则同态的一种函数方法

IF 1.5 1区数学

Algebraic Geometry Pub Date : 2019-11-22 DOI: 10.14231/ag-2023-003

Jeff Achter, Sebastian Casalaina-Martin, Charles Vial

{"title":"A functorial approach to regular homomorphisms","authors":"Jeff Achter, Sebastian Casalaina-Martin, Charles Vial","doi":"10.14231/ag-2023-003","DOIUrl":"https://doi.org/10.14231/ag-2023-003","url":null,"abstract":"Classically, regular homomorphisms have been defined as a replacement for Abel--Jacobi maps for smooth varieties over an algebraically closed field. In this work, we interpret regular homomorphisms as morphisms from the functor of families of algebraically trivial cycles to abelian varieties and thereby define regular homomorphisms in the relative setting, e.g., families of schemes parameterized by a smooth variety over a given field. In that general setting, we establish the existence of an initial regular homomorphism, going by the name of algebraic representative, for codimension-2 cycles on a smooth proper scheme over the base. This extends a result of Murre for codimension-2 cycles on a smooth projective scheme over an algebraically closed field. In addition, we prove base change results for algebraic representatives as well as descent properties for algebraic representatives along separable field extensions. In the case where the base is a smooth variety over a subfield of the complex numbers we identify the algebraic representative for relative codimension-2 cycles with a subtorus of the intermediate Jacobian fibration which was constructed in previous work. \u0000At the heart of our descent arguments is a base change result along separable field extensions for Albanese torsors of separated, geometrically integral schemes of finite type over a field.","PeriodicalId":48564,"journal":{"name":"Algebraic Geometry","volume":" ","pages":""},"PeriodicalIF":1.5,"publicationDate":"2019-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46252869","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}