Parametrization of geometric Beilinson--Bloch heights via adelic line bundles
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866914065227448320 |
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| author | Song, Yinchong |
| author_facet | Song, Yinchong |
| contents | Let $ S $ be a quasi-projective smooth variety over complex field $ \mathbb{C} $. For a smooth projective morphism $ π:X\to S $, we will introduce a new height pairing \begin{align*} CH^p_{\hom}(X/S) \times CH^q_{\hom}(X/S) \to \widetilde{\mathrm{Pic}}(S) \end{align*} with $ \widetilde{\mathrm{Pic}}(S) $ the group of geometric adelic line bundles in the sense of Yuan--Zhang. It essentially parametrizes the asymptotic height pairing introduced by Brosnan and Pearlstein. We will show that this asymptotic height pairing coincides with Beilinson--Bloch pairing under certain conditions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_19912 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Parametrization of geometric Beilinson--Bloch heights via adelic line bundles Song, Yinchong Algebraic Geometry Number Theory Let $ S $ be a quasi-projective smooth variety over complex field $ \mathbb{C} $. For a smooth projective morphism $ π:X\to S $, we will introduce a new height pairing \begin{align*} CH^p_{\hom}(X/S) \times CH^q_{\hom}(X/S) \to \widetilde{\mathrm{Pic}}(S) \end{align*} with $ \widetilde{\mathrm{Pic}}(S) $ the group of geometric adelic line bundles in the sense of Yuan--Zhang. It essentially parametrizes the asymptotic height pairing introduced by Brosnan and Pearlstein. We will show that this asymptotic height pairing coincides with Beilinson--Bloch pairing under certain conditions. |
| title | Parametrization of geometric Beilinson--Bloch heights via adelic line bundles |
| topic | Algebraic Geometry Number Theory |
| url | https://arxiv.org/abs/2406.19912 |