Theta cycles and the Beilinson--Bloch--Kato conjectures
| Autor: | Disegni, Daniel |
|---|---|
| Rok vydání: | 2023 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1016/j.jnt.2024.04.001 |
| Popis: | We introduce `canonical' classes in the Selmer groups of certain Galois representations with a conjugate-symplectic symmetry. They are images of special cycles in unitary Shimura varieties, and defined uniquely up to a scalar. The construction is a slight refinement of one of Y. Liu, based on the conjectural modularity of Kudla's theta series of special cycles. For 2-dimensional representations, Theta cycles are (the Selmer images of) Heegner points. In general, they conjecturally exhibit an analogous strong relation with the Beilinson--Bloch--Kato conjectures in rank 1, for which we gather the available evidence. Comment: 24 pages, final version, to appear in Journal of Number Theory (special issue: Proceedings of the Second JNT Biennial Conference 2022) |
| Databáze: | arXiv |
| Externí odkaz: |
|