题目：Kolyvagin conjecture and Markov Chains

报告人：潘锦钊 同济大学

时间：2025年6月10日（星期二）16:00-17:00

地点：东区第五教学楼5205教室

摘要：Kolyvagin conjecture is about arithmetic behavior of quadratic twists of elliptic curves. Roughly speaking, for any prime p, there exists a member in a given quadratic family and its isogeny classes with trivial p-part of Shafarevich-Tate group and rank 0 (resp. rank 1). For p=2, we found that this conjecture is closely related to Markov chain property of 2-Selmer groups and solved the conjecture when elliptic curves have full rational 2-torsion points. This is a joint work with Ye Tian.