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summer 2000
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Wojciech J. Gajda

professor of mathematics

Mailing address:
Faculty of Mathematics and Computer Science
Adam Mickiewicz University
Umultowska 87, 61-614 Poznań, POLAND
Office: Collegium Mathematicum, B1-35
Phone: +48 (61) 829 5503
Fax: +48 (61) 829 5315
Email: gajda AT amu DOT edu DOT pl

Research interests:

arithmetic geometry, number theory, algebraic topology, algebraic K-theory


Matteo Longo, Università degli Studi di Padova

15.01.2020 12:00, B1-37

Title: The Kolyvagin Conjecture for modular forms


Kolyvagin conjecture for elliptic curves was formulated by V.Kolyvagin in the nineties, and predicts the non-triviality of certain cohomology classes costructed from Heegner points. Consequences of this conjecture include the p-part of the Birch and Swinnerton-Dyer conjecture, parity results, and a precise description of the structure of the Tate-Shafarevich group of the elliptic curve. The original conjecture is now a theorem by the work of many people, including W.Zhang, C.Skinner and R.Venerucci. We investigate an analogue of Kolyvagin Conjecture for higher weight modular forms in which Heegner points are replaced by Heegner cycles on Kuga-Sato varieties. As a consequence, we obtain some results on the structure of the Tate-Shafarevich group attached to the modular form, and a p-part of a Bloch-Kato conjecture in analytic rank 1. This is a work in collaboration with Stefano Vigni.