Details
Original language | English |
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Publication status | E-pub ahead of print - 20 Jun 2024 |
Abstract
Keywords
- math.AG, math.NT, 14C15, 14C25
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2024.
Research output: Working paper/Preprint › Preprint
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TY - UNPB
T1 - Cycle conjectures and birational invariants over finite fields
AU - Balkan, Samet
AU - Schreieder, Stefan
N1 - 33 pages
PY - 2024/6/20
Y1 - 2024/6/20
N2 - 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.
AB - 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.
KW - math.AG
KW - math.NT
KW - 14C15, 14C25
M3 - Preprint
BT - Cycle conjectures and birational invariants over finite fields
ER -