Theta cycles and the Beilinson--Bloch--Kato conjectures
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866908863451627520 |
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| author | Disegni, Daniel |
| author_facet | Disegni, Daniel |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2303_17817 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Theta cycles and the Beilinson--Bloch--Kato conjectures Disegni, Daniel Number Theory 11G40, 11F27, 11G18, 11G50, 11F80 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. |
| title | Theta cycles and the Beilinson--Bloch--Kato conjectures |
| topic | Number Theory 11G40, 11F27, 11G18, 11G50, 11F80 |
| url | https://arxiv.org/abs/2303.17817 |