Differentiability of Relative Volumes Over an Arbitrary Non-Archimedean Field
Keyword(s):
Abstract Given an ample line bundle $L$ on a geometrically reduced projective scheme defined over an arbitrary non-Archimedean field, we establish a differentiability property for the relative volume of two continuous metrics on the Berkovich analytification of $L$, extending previously known results in the discretely valued case. As applications, we provide fundamental solutions to certain non-Archimedean Monge–Ampère equations and generalize an equidistribution result for Fekete points. Our main technical input comes from determinant of cohomology and Deligne pairings.
2017 ◽
Vol 50
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pp. 545-578
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pp. 1460029
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pp. 5769-5782
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1989 ◽
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pp. 105-123
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pp. 6089-6112
2007 ◽
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pp. 323-342
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