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- W1621396586 abstract "A singular curve over a non-perfect field K may not have a smooth model over K. Those are said to genus. If K is a global field of positive characteristic and C/K a curve that change genus, then C(K) is known to be finite. The purpose of this note is to give examples of curves with fixed relative genus, defined over K for which #C(K) is arbitrarily large. The motivation for considering this problem comes from the work of Caporaso et al. [CHM], where they show that a conjecture of Lang implies that, for a number field K, #C(K) can be bounded in terms of g and K only for all curves C/K of genus g > 1." @default.
- W1621396586 created "2016-06-24" @default.
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- W1621396586 date "1995-06-06" @default.
- W1621396586 modified "2023-09-27" @default.
- W1621396586 title "Curves that change genus can have arbitrarily many rational points" @default.
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