Geodesic
A rigid analytic proof that the Abel–Jacobi map extends to compact-type models
Canadian mathematical bulletin, Tome 67 (2024) no. 3, pp. 648-654

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DOI

Let K be a non-Archimedean valued field with valuation ring R. Let $C_\eta $ be a K-curve with compact-type reduction, so its Jacobian $J_\eta $ extends to an abelian R-scheme J. We prove that an Abel–Jacobi map $\iota \colon C_\eta \to J_\eta $ extends to a morphism $C\to J$, where C is a compact-type R-model of J, and we show this is a closed immersion when the special fiber of C has no rational components. To do so, we apply a rigid-analytic “fiberwise” criterion for a morphism to extend to integral models, and geometric results of Bosch and Lütkebohmert on the analytic structure of $J_\eta $.
DOI : 10.4153/S0008439524000031
Mots-clés : Abel–jacobi, bad reduction, tropical, non-Archimedean 
Dupuy, Taylor; Rabinoff, Joseph. A rigid analytic proof that the Abel–Jacobi map extends to compact-type models. Canadian mathematical bulletin, Tome 67 (2024) no. 3, pp. 648-654. doi: 10.4153/S0008439524000031
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     title = {A rigid analytic proof that the {Abel{\textendash}Jacobi} map extends to compact-type models},
     journal = {Canadian mathematical bulletin},
     pages = {648--654},
     year = {2024},
     volume = {67},
     number = {3},
     doi = {10.4153/S0008439524000031},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008439524000031/}
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