Admettant l'hypothèse de Schinzel et la finitude des groupes de Tate–Shafarevich des courbes elliptiques sur les corps de nombres, toute intersection lisse de deux quadriques dans l'espace projectif de dimension n satisfait au principe de Hasse si
Assuming Schinzel's hypothesis and the finiteness of Tate–Shafarevich groups of elliptic curves over number fields, smooth intersections of two quadrics in n-dimensional projective space satisfy the Hasse principle if
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Olivier Wittenberg 1
@article{CRMATH_2006__342_4_223_0, author = {Olivier Wittenberg}, title = {Principe de {Hasse} pour les intersections de deux quadriques}, journal = {Comptes Rendus. Math\'ematique}, pages = {223--227}, publisher = {Elsevier}, volume = {342}, number = {4}, year = {2006}, doi = {10.1016/j.crma.2005.12.005}, language = {fr}, }
Olivier Wittenberg. Principe de Hasse pour les intersections de deux quadriques. Comptes Rendus. Mathématique, Volume 342 (2006) no. 4, pp. 223-227. doi : 10.1016/j.crma.2005.12.005. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2005.12.005/
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- A threefold violating a local-to-global principle for rationality, Research in Number Theory, Volume 10 (2024) no. 2 | DOI:10.1007/s40993-024-00515-8
- On the number of certain del Pezzo surfaces of degree four violating the Hasse principle, Journal of Number Theory, Volume 162 (2016), p. 224 | DOI:10.1016/j.jnt.2015.10.018
- Effective Hasse principle for the intersection of two quadrics, LMS Journal of Computation and Mathematics, Volume 19 (2016) no. A, p. 73 | DOI:10.1112/s146115701600022x
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