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- W3081778768 abstract "For a $d$-dimensional smooth projective variety $X$ over the function field of a smooth variety $B$ over a field $k$ and for $ige 0$, we define a subgroup $CH^i(X)^{(0)}$ of $CH^i(X)$ and construct a height [CH^i(X)^{(0)}times CH^{d+1-i}(X)^{(0)}to CH^1(B)] in the category of abelian groups modulo isogeny. For $i=1,d$, $CH^i(X)^{(0)}$ is the group of cycles numerically equivalent to $0$. This pairing relates to pairings defined by P. Schneider and A. Beilinson if $B$ is a curve, to a refined height defined by L. Moret-Bailly when $X$ is an abelian variety, and to a pairing with values in $H^2(B_{bar k},mathbf{Q}_l(1))$ defined by D. Rossler and T. Szamuely in general. We study it in detail when $i=1$." @default.
- W3081778768 created "2020-09-08" @default.
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- W3081778768 date "2020-09-01" @default.
- W3081778768 modified "2023-09-27" @default.
- W3081778768 title "Refined height pairing" @default.
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