Rigid analytic p-adic Simpson correspondence for line bundles
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Publication:6351862
DOI10.1007/S40304-021-00256-5arXiv2010.10825MaRDI QIDQ6351862
Publication date: 21 October 2020
Abstract: The p-adic Simpson correspondence due to Faltings is a p-adic analogue of non-abelian Hodge theory. The following is the main result of this article: The correspondence for line bundles can be enhanced to a rigid analytic morphism of moduli spaces under certain smallness conditions. In the complex setting, Simpson shows that there is a complex analytic morphism from the moduli space for the vector bundles with integrable connection to the moduli space of representations of a finitely generated group as algebraic varieties. We give a p-adic analogue of Simpson's result.
Algebraic moduli problems, moduli of vector bundles (14D20) Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials (14F10) Vector bundles on curves and their moduli (14H60) Homotopy theory and fundamental groups in algebraic geometry (14F35) Rigid analytic geometry (14G22) (p)-adic cohomology, crystalline cohomology (14F30) Fine and coarse moduli spaces (14D22)
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