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Titlebook: Rigid Geometry of Curves and Their Jacobians; Werner Lütkebohmert Book 2016 Springer International Publishing Switzerland 2016 Algebraic G

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https://doi.org/10.1007/978-3-319-27371-6Algebraic Geometry; Arithmetic Geometry; Number Theory; Several Complex Variables and Analytic Spaces; C
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Formal and Rigid Geometry, introduced such spaces in Bosch (Manuscr. Math. 20:1–27, .)..In Sect. . admissible formal .-schemes and formal blowing-ups are defined. In a canonical way the generic fiber of an admissible formal .-scheme is a formal analytic space..In Sect. . we will discuss the important result in Theorem . of R
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Rigid Analytic Curves,rd (in Publ. Math. IHES 36:75–109, .), see also Raynaud (in Proceedings of the Conference on Fundamental Groups of Curves in Algebraic Geometry Held in Luminy, vol. 187, .; Chap. 5)..In Sect. . the result on the periphery is used to constitute a genus formula in Proposition . which relates the genus
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Jacobian Varieties,. with semi-abelian reduction. . is a formal torus extension of a formal abelian .-scheme . with reduction ...The generic fiber . of . is the largest connected open subgroup of . which admits a smooth formal .-model; this is discussed in Sect. . in a more general context. The relationship between th
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Raynaud Extensions,cial interest are the polarizations of Jacobians .. There are two, the usual theta polarization and the canonical polarization which is related to a pairing on the homology group . of the curve .. In Sect. . we discuss these polarizations. This is related to Riemann’s vanishing theorem Corollary . f
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