Varieties over $\bar{\mathbb{Q}}$ with infinite Chow groups modulo almost all primes
Fuente:
arXiv
Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2023
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866929225764700160 |
|---|---|
| author | Scavia, Federico |
| author_facet | Scavia, Federico |
| contents | Let $E$ be the Fermat cubic curve over $\bar{\mathbb{Q}}$. In 2002, Schoen proved that the group $CH^2(E^3)/\ell$ is infinite for all primes $\ell\equiv 1\pmod 3$. We show that $CH^2(E^3)/\ell$ is infinite for all prime numbers $\ell> 5$. This gives the first example of a smooth projective variety $X$ over $\bar{\mathbb{Q}}$ such that $CH^2(X)/\ell$ is infinite for all but at most finitely many primes $\ell$. A key tool is a recent theorem of Farb--Kisin--Wolfson, whose proof uses the prismatic cohomology of Bhatt--Scholze. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_05729 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Varieties over $\bar{\mathbb{Q}}$ with infinite Chow groups modulo almost all primes Scavia, Federico Algebraic Geometry 14C15 (Primary) 14C25, 14K05, 14K22 (Secondary) Let $E$ be the Fermat cubic curve over $\bar{\mathbb{Q}}$. In 2002, Schoen proved that the group $CH^2(E^3)/\ell$ is infinite for all primes $\ell\equiv 1\pmod 3$. We show that $CH^2(E^3)/\ell$ is infinite for all prime numbers $\ell> 5$. This gives the first example of a smooth projective variety $X$ over $\bar{\mathbb{Q}}$ such that $CH^2(X)/\ell$ is infinite for all but at most finitely many primes $\ell$. A key tool is a recent theorem of Farb--Kisin--Wolfson, whose proof uses the prismatic cohomology of Bhatt--Scholze. |
| title | Varieties over $\bar{\mathbb{Q}}$ with infinite Chow groups modulo almost all primes |
| topic | Algebraic Geometry 14C15 (Primary) 14C25, 14K05, 14K22 (Secondary) |
| url | https://arxiv.org/abs/2307.05729 |