On p-adic height pairings
On p-adic height pairings
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关于 p 进高度配对
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发表时间：
2002
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通讯作者：
J. Nekovář
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作者：
J. Nekovář
目前的工作的目的是构造p-adic高度配对在一个足够一般的设置，即塞尔默群的合理行为的p-adic伽罗瓦表示数域。这些配对，模一般代数上同调，诱导高度配对之间（同调平凡）代数循环的每一个适当的光滑品种定义在一个数域。对于在所有素数p处都具有良好约化的光滑射影簇，我们的构造只需要一个上同调假设：我们必须假设某些etale上同调群的纯度猜想在给定簇的所有不良约化的地方都成立。更具体地说，设X是定义在数域K上的维数为d的真光滑簇。记CH（X）0为X上余维数为i的同调平凡代数圈群，定义在K上，模有理等价。如果i+ j = d+ 1，则存在“etale Abel-Jacobi映射”，
The aim of the present work is to construct p-adic height pairings in a sufficiently general setting, namely for Selmer groups of reasonably behaved p-adic Galois representations over number fields. These pairings should, modulo general conjectures on etale cohomology, induce height pairings between (homologically trivial) algebraic cycles on every proper smooth variety defined over a number field. For smooth projective varieties with good reduction at all primes dividing p, our construction requires only one cohomological assumption: we have to assume that the purity conjecture for certain etale cohomology group holds at all places of bad reduction of the given variety. More specifically, let X be a proper smooth variety, of dimension d, defined over a number field K. Write CH(X)0 for the group of homologically trivial algebraic cycles of codimension i on X, defined over K, modulo rational equivalence. If i+ j = d+ 1, then there are “etale Abel-Jacobi maps”