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- W2275143344 abstract "We adapt for algebraically closed fields $k$ of characteristic greater than $2$ two results of Voisin, on the decomposition of the diagonal of a smooth cubic hypersurface $X$ of dimension $3$ over $mathbb C$, namely: the equivalence between Chow-theoretic and cohomological decompositions of the diagonal of those hypersurfaces and the fact that the algebraicity (with $mathbb Z_2$-coefficients) of the minimal class $theta^4/4!$ of the intermediate jacobian $J(X)$ of $X$ implies the Chow-theoretic decomposition of the diagonal of $X$. Using the second result, the Tate conjecture for divisors on surfaces defined over finite fields predicts, via a theorem of Schoen, that every smooth cubic hypersurface of dimension $3$ over the algebraic closure of a finite field of characteristic $>2$ admits a Chow-theoretic decomposition of the diagonal." @default.
- W2275143344 created "2016-06-24" @default.
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- W2275143344 date "2016-02-22" @default.
- W2275143344 modified "2023-09-25" @default.
- W2275143344 title "On the universal $mathrm{CH}_0$ group of cubic threefolds in positive characteristic" @default.
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