On some modified Tate-Shafarevich groups

Abstract: We describe two local-global questions generalizing some classical ones considered by Hasse and Cassels, respectively. Along with explaining the relationship between these two problems, we depict some modified Tate-Shafarevich groups whose vanishings imply an affirmative answer to both of them. We also give an overview of the most recent results achieved for the two problems.

number theory

Audience: researchers in the topic

London number theory seminar

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