{"docId":6460,"paperId":6460,"url":"https:\/\/hrj.episciences.org\/6460","doi":"10.46298\/hrj.2020.6460","journalName":"Hardy-Ramanujan Journal","issn":"","eissn":"2804-7370","volume":[{"vid":404,"name":"Volume 42 - Special Commemorative volume in honour of Alan Baker - 2019"}],"section":[],"repositoryName":"Hal","repositoryIdentifier":"hal-02554271","repositoryVersion":1,"repositoryLink":"https:\/\/hal.archives-ouvertes.fr\/hal-02554271v1","dateSubmitted":"2020-05-07 12:37:53","dateAccepted":"2020-05-19 20:20:37","datePublished":"2020-05-20 21:56:53","titles":{"en":"Divisibility of Selmer groups and class groups"},"authors":["Banerjee, Kalyan","Chakraborty, Kalyan","Hoque, Azizul"],"abstracts":{"en":"In this paper, we study two topics. One is the divisibility problem of class groups of quadratic number fields and its connections to algebraic geometry. The other is the construction of Selmer group and Tate-Shafarevich group for an abelian variety defined over a number field."},"keywords":[{"en":"Abelian variety 2010"},{"en":"Hyperelliptic surface"},{"en":"Imaginary quadratic field"},{"en":"Selmer group"},{"en":"Tate-Shafarevich group"},{"en":"Chow group"},{"en":"Class group"},{"en":"Picard group"},"[MATH]Mathematics [math]","[MATH.MATH-NT]Mathematics [math]\/Number Theory [math.NT]"]}