An arithmetic variant of Raynaud's theorem
J Love, L Taylor - arXiv preprint arXiv:2009.10284, 2020 - arxiv.org
J Love, L Taylor
arXiv preprint arXiv:2009.10284, 2020•arxiv.orgIt is well known that for a regular semistable curve $\mathfrak X $ over a DVR with
algebraically closed residue field, the spanning trees of the dual graph of the special fiber of
$\mathfrak X $ are in bijection with components of the special fiber of the N\'eron model of
the Jacobian of $\mathfrak X $. We prove a generalization of this fact that does not require
the residue field to be algebraically closed, using a combinatorially enriched version of the
dual graph to encode arithmetic information about divisors on $\mathfrak X $.
algebraically closed residue field, the spanning trees of the dual graph of the special fiber of
$\mathfrak X $ are in bijection with components of the special fiber of the N\'eron model of
the Jacobian of $\mathfrak X $. We prove a generalization of this fact that does not require
the residue field to be algebraically closed, using a combinatorially enriched version of the
dual graph to encode arithmetic information about divisors on $\mathfrak X $.
It is well known that for a regular semistable curve over a DVR with algebraically closed residue field, the spanning trees of the dual graph of the special fiber of are in bijection with components of the special fiber of the N\'eron model of the Jacobian of . We prove a generalization of this fact that does not require the residue field to be algebraically closed, using a combinatorially enriched version of the dual graph to encode arithmetic information about divisors on .
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