geometric rank
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2017 ◽  
Vol 54 (3) ◽  
pp. 807-820
Author(s):  
Daniele Ettore Otera
Keyword(s):  

2014 ◽  
Vol 152 (1-2) ◽  
pp. 189-200
Author(s):  
Ashwin Arulselvan

2013 ◽  
Vol 149 (11) ◽  
pp. 1818-1838 ◽  
Author(s):  
Eric Katz ◽  
David Zureick-Brown

AbstractLet $X$ be a curve over a number field $K$ with genus $g\geq 2$, $\mathfrak{p}$ a prime of ${ \mathcal{O} }_{K} $ over an unramified rational prime $p\gt 2r$, $J$ the Jacobian of $X$, $r= \mathrm{rank} \hspace{0.167em} J(K)$, and $\mathscr{X}$ a regular proper model of $X$ at $\mathfrak{p}$. Suppose $r\lt g$. We prove that $\# X(K)\leq \# \mathscr{X}({ \mathbb{F} }_{\mathfrak{p}} )+ 2r$, extending the refined version of the Chabauty–Coleman bound to the case of bad reduction. The new technical insight is to isolate variants of the classical rank of a divisor on a curve which are better suited for singular curves and which satisfy Clifford’s theorem.


2004 ◽  
Vol 8 (2) ◽  
pp. 233-258 ◽  
Author(s):  
Dekang Xu ◽  
Shanyu Yi
Keyword(s):  

1978 ◽  
Vol 21 (3) ◽  
pp. 273-283 ◽  
Author(s):  
Hien Q. Nguyen

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