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- W87702284 abstract "Classical results of Weil, Neron and Tate are generalized to local heights of subvarieties with respect to hermitian pseudo-divisors. The local heights are well-defined if the intersection of supports is empty. In the archimedean case, the metrics are hermitian and the local heights are defined by a refined version of the *-product of Gillet-Soule developped on compact varieties without assuming regularity. In the non-archimedean case, the local heights are intersection numbers using methods from rigid and formal geometry to handle non-discrete valuations. To include canonical metrics of line bundles algebraically equivalent to 0, a local Chow cohomology is introduced on formal models over the valuation ring. Using Tate’s limit argument, canonical local heights of subvarieties on an abelian variety are obtained with respect to any pseudo-divisors. By integration over an M-field, we deduce corresponding results for global heights of subvarieties." @default.
- W87702284 created "2016-06-24" @default.
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- W87702284 date "2003-01-01" @default.
- W87702284 modified "2023-09-23" @default.
- W87702284 title "Local and canonical heights of subvarieties" @default.
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