Soit une variété arithmétique projective régulière munie d’un fibré en droites hermitien ample . On montre que la proportion des sections globales avec de dont le diviseur n’a pas de point singulier sur la fibre pour tout nombre premier tend vers quand .
Let be a regular projective arithmetic variety equipped with an ample Hermitian line bundle . We prove that the proportion of global sections with of whose divisor does not have a singular point on the fiber over any prime tends to as .
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Keywords: Bertini theorem, Arakelov geometry, arithmetic ampleness
Mot clés : Théorème de Bertini, géométrie d’Arakelov, amplitude arithmétique
@article{JEP_2022__9__601_0, author = {Wang, Xiaozong}, title = {On the {Bertini} regularity theorem for arithmetic varieties}, journal = {Journal de l{\textquoteright}\'Ecole polytechnique {\textemdash} Math\'ematiques}, pages = {601--670}, publisher = {Ecole polytechnique}, volume = {9}, year = {2022}, doi = {10.5802/jep.191}, language = {en}, url = {http://www.numdam.org/articles/10.5802/jep.191/} }
TY - JOUR AU - Wang, Xiaozong TI - On the Bertini regularity theorem for arithmetic varieties JO - Journal de l’École polytechnique — Mathématiques PY - 2022 SP - 601 EP - 670 VL - 9 PB - Ecole polytechnique UR - http://www.numdam.org/articles/10.5802/jep.191/ DO - 10.5802/jep.191 LA - en ID - JEP_2022__9__601_0 ER -
Wang, Xiaozong. On the Bertini regularity theorem for arithmetic varieties. Journal de l’École polytechnique — Mathématiques, Tome 9 (2022), pp. 601-670. doi : 10.5802/jep.191. http://www.numdam.org/articles/10.5802/jep.191/
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