Strong arithmetic Shafarevich conjecture for semistable curves
Strong arithmetic Shafarevich conjecture for semistable curves
Let be a field as above, and let be an ideal of the field . Strong arithmetic Shafarevich conjecture. There exists a finite extension of and a semistable model of such that the ring is a direct sum of finitely many fields for every such ideal . This is proposed as a strong arithmetic analogue of Shafarevich's conjecture; the source does not state what is known or whether it has been resolved.
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Primary source
Fedor Bogomolov and Ludmil Katzarkov, “Complex projective surfaces and infinite groups”, arXiv:alg-geom/9703002 (1997).
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