Cycle conjectures and birational invariants over finite fields
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866917161135505408 |
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| author | Balkan, Samet Schreieder, Stefan |
| author_facet | Balkan, Samet Schreieder, Stefan |
| contents | We study a natural birational invariant for varieties over finite fields and show that its vanishing on projective space is equivalent to the Tate conjecture, the Beilinson conjecture, and the Grothendieck--Serre semi-simplicity conjecture for all smooth projective varieties over finite fields. We further show that the Tate, Beilinson, and 1-semi-simplicity conjecture in half of the degrees implies those conjectures in all degrees. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_14438 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Cycle conjectures and birational invariants over finite fields Balkan, Samet Schreieder, Stefan Algebraic Geometry Number Theory 14C15, 14C25 We study a natural birational invariant for varieties over finite fields and show that its vanishing on projective space is equivalent to the Tate conjecture, the Beilinson conjecture, and the Grothendieck--Serre semi-simplicity conjecture for all smooth projective varieties over finite fields. We further show that the Tate, Beilinson, and 1-semi-simplicity conjecture in half of the degrees implies those conjectures in all degrees. |
| title | Cycle conjectures and birational invariants over finite fields |
| topic | Algebraic Geometry Number Theory 14C15, 14C25 |
| url | https://arxiv.org/abs/2406.14438 |