The growth of Tate-Shafarevich groups in cyclic extensions
发布时间：2023年03月20日
浏览次数：2641
发布者: Biao Ma
主讲人： 谢建峰（BICMR）
活动时间： 从 2023-03-27 15:00 到 16:30
场地： 北京国际数学研究中心，全斋全29教室
Let K be a global field and p be a prime number with p≠char K. A classical theorem in algebraic number theory asserts that when L varies in Z/pZ-extensions of K, the p-rank of the class group of L is unbounded. It is expected that similar unboundenss result also holds for other arithmetic objects. Based on Cassels-Poitou-Tate sequence, K. Česnavičius proved that for fixed abelian variety A over K, the p-Selmer group of A over L is unbounded when L varies in Z/pZ-extensions of K. He raised a further problem: in the same setting, does the Tate-Shafarevich group of A also grow unboundedly? Using a machinery developed by B. Mazur and K. Rubin, we give a positive answer to this problem. This is a joint work with Yi Ouyang.
