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- W3110917838 abstract "Abstract For a smooth rigid space X over a perfectoid field extension K of $mathbb {Q}_p$ , we investigate how the v -Picard group of the associated diamond $X^{diamondsuit }$ differs from the analytic Picard group of X . To this end, we construct a left-exact ‘Hodge–Tate logarithm’ sequence $$begin{align*}0to operatorname{Pic}_{mathrm{an}}(X)to operatorname{Pic}_v(X^{diamondsuit})to H^0(X,Omega_X^1){-1}. end{align*}$$ We deduce some analyticity criteria which have applications to p -adic modular forms. For algebraically closed K , we show that the sequence is also right-exact if X is proper or one-dimensional. In contrast, we show that, for the affine space $mathbb {A}^n$ , the image of the Hodge–Tate logarithm consists precisely of the closed differentials. It follows that, up to a splitting, v -line bundles may be interpreted as Higgs bundles. For proper X , we use this to construct the p -adic Simpson correspondence of rank one." @default.
- W3110917838 created "2020-12-21" @default.
- W3110917838 creator A5025516935 @default.
- W3110917838 date "2022-01-01" @default.
- W3110917838 modified "2023-09-30" @default.
- W3110917838 title "Line bundles on rigid spaces in the<i>v</i>-topology" @default.
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- W3110917838 doi "https://doi.org/10.1017/fms.2022.72" @default.
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