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Monogenic cubic fields and local obstructions

By Ari Shnidman

Appears in collection : Zeta Functions / Fonctions Zêta

A number field is monogenic if its ring of integers is generated by a single element. It is conjectured that for any degree d > 2, the proportion of degree d number fields which are monogenic is 0. There are local obstructions that force this proportion to be < 100%, but beyond this very little is known. I’ll discuss work with Alpoge and Bhargava showing that a positive proportion of cubic fields (d = 3) have no local obstructions and yet are still not monogenic. This uses new results on ranks of Selmer groups of elliptic curves in twist families.

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Citation data

  • DOI 10.24350/CIRM.V.19586203
  • Cite this video Shnidman Ari (12/5/19). Monogenic cubic fields and local obstructions. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19586203
  • URL https://dx.doi.org/10.24350/CIRM.V.19586203


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