We prove finiteness results for Tate–Shafarevich groups in degree associated with -motives. We give a number-theoretic interpretation of these groups, relate them to Leopoldt’s conjecture, and present an example of a semiabelian variety with an infinite Tate–Shafarevich group in degree . We also establish an arithmetic duality theorem for -motives over number fields, which complements earlier results of Harari and Szamuely.
"On the second Tate–Shafarevich group of a 1-motive." Algebra Number Theory 7 (10) 2511 - 2544, 2013. https://doi.org/10.2140/ant.2013.7.2511