Hilbert properties under base change in small extensions

Autor: Bary-Soroker, Lior, Fehm, Arno, Petersen, Sebastian

We study the preservation of the Hilbert property and of the weak Hilbert property under base change in field extensions. In particular we show that these properties are preserved if the extension is finitely generated or Galois with finitely generat

Externí odkaz: http://arxiv.org/abs/2312.16219

Many cubic surfaces contain rational points

Autor: Browning, T. D.

Publikováno v: Mathematika 63 (2017) 818-839

Building on recent work of Bhargava--Elkies--Schnidman and Kriz--Li, we produce infinitely many smooth cubic surfaces defined over the field of rational numbers that contain rational points.
Comment: 23 pages; minor edits and added new remark (R

Externí odkaz: http://arxiv.org/abs/1701.00525

Bornes effectives pour la torsion des courbes elliptiques sur les corps de nombres

Autor: Parent, Pierre

In this paper we give a detailed proof of a result we announced a year ago. This result is an effective version of the theorem of Mazur-Kamienny-Merel concerning uniform bounds for rational torsion points on elliptic curves over number fields.
C

Externí odkaz: http://arxiv.org/abs/alg-geom/9611022

Many cubic surfaces contain rational points

Autor: Tim D Browning

Publikováno v: Browning, T 2017, ' Many cubic surfaces contain rational points ', Mathematika, vol. 63, no. 3 . https://doi.org/10.1112/S0025579317000195

Building on recent work of Bhargava--Elkies--Schnidman and Kriz--Li, we produce infinitely many smooth cubic surfaces defined over the field of rational numbers that contain rational points.
23 pages; minor edits and added new remark (Remark 2.1

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::d368ee2b0367fba5bc44ce4660b8374b
http://arxiv.org/abs/1701.00525