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326
Uniformization of DeligneMumford curves
, 2005
"... We compute the fundamental groups of nonsingular analytic DeligneMumford curves, classify the simply connected ones, and classify analytic DeligneMumford curves by their uniformization type. As a result, we find an explicit presentation of an arbitrary DeligneMumford curve as a quotient stack. ..."
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We compute the fundamental groups of nonsingular analytic DeligneMumford curves, classify the simply connected ones, and classify analytic DeligneMumford curves by their uniformization type. As a result, we find an explicit presentation of an arbitrary DeligneMumford curve as a quotient stack
ALGORITHMS FOR MUMFORD CURVES
"... Abstract. Mumford showed that Schottky subgroups of PGL(2,K) give rise to certain curves, now called Mumford curves, over a nonArchimedean field K. Such curves are foundational to subjects dealing with nonArchimedean varieties, including Berkovich theory and tropical geometry. We develop and impl ..."
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Abstract. Mumford showed that Schottky subgroups of PGL(2,K) give rise to certain curves, now called Mumford curves, over a nonArchimedean field K. Such curves are foundational to subjects dealing with nonArchimedean varieties, including Berkovich theory and tropical geometry. We develop
COUNTING PLANE MUMFORD CURVES
, 811
"... Abstract. A padic version of GromovWitten invariants for counting plane curves of genus g and degree d through a given number of points is discussed. The multiloop version of padic string theory considered by Chekhov and others motivates us to ask how many of these curves are Mumford curves, i.e. ..."
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Abstract. A padic version of GromovWitten invariants for counting plane curves of genus g and degree d through a given number of points is discussed. The multiloop version of padic string theory considered by Chekhov and others motivates us to ask how many of these curves are Mumford curves, i
Counting plane Mumford curves
"... A padic version of GromovWitten invariants for counting plane curves of genus g and degree d through a given number of points is discussed. The multiloop version of padic string theory considered by Chekhov and others motivates us to ask how many of these curves are Mumford curves, i.e. uniformis ..."
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A padic version of GromovWitten invariants for counting plane curves of genus g and degree d through a given number of points is discussed. The multiloop version of padic string theory considered by Chekhov and others motivates us to ask how many of these curves are Mumford curves, i
MODULAR INDEX INVARIANTS OF MUMFORD CURVES
, 2011
"... Modular index invariants of Mumford curves We continue an investigation initiated by Consani–Marcolli of the relation between the algebraic geometry of padic Mumford curves and the noncommutative geometry of graph C∗algebras associated to the action of the uniformizing padic Schottky group on the ..."
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Modular index invariants of Mumford curves We continue an investigation initiated by Consani–Marcolli of the relation between the algebraic geometry of padic Mumford curves and the noncommutative geometry of graph C∗algebras associated to the action of the uniformizing padic Schottky group
ON ABELIAN AUTOMORPHISM GROUPS OF MUMFORD CURVES
, 2008
"... Abstract. We use rigid analytic uniformization by Schottky groups to give a bound for the order of the abelian subgroups of the automorphism group of a Mumford curve in terms of its genus. ..."
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Abstract. We use rigid analytic uniformization by Schottky groups to give a bound for the order of the abelian subgroups of the automorphism group of a Mumford curve in terms of its genus.
MODULAR INDEX INVARIANTS OF MUMFORD CURVES
, 2009
"... We continue an investigation initiated by Consani–Marcolli of the relation between the algebraic geometry of padic Mumford curves and the noncommutative geometry of graph C ∗algebras associated to the action of the uniformizing padic Schottky group on the Bruhat–Tits tree. We reconstruct invarian ..."
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Cited by 2 (2 self)
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We continue an investigation initiated by Consani–Marcolli of the relation between the algebraic geometry of padic Mumford curves and the noncommutative geometry of graph C ∗algebras associated to the action of the uniformizing padic Schottky group on the Bruhat–Tits tree. We reconstruct
Equivariant deformation of Mumford curves and
, 2001
"... of ordinary curves in positive characteristic ..."
Spectral triples from Mumford curves
, 2003
"... We construct spectral triples associated to Schottky–Mumford curves, in such a way that the local Euler factor can be recovered from the zeta functions of such spectral triples. We propose a way of extending this construction to the case where the curve is not ksplit degenerate. ..."
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Cited by 11 (7 self)
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We construct spectral triples associated to Schottky–Mumford curves, in such a way that the local Euler factor can be recovered from the zeta functions of such spectral triples. We propose a way of extending this construction to the case where the curve is not ksplit degenerate.
MUMFORD CURVES WITH MAXIMAL AUTOMORPHISM GROUP
, 2002
"... Abstract. It is known that a Mumford curve of genus g / ∈ {5, 6,7, 8} over a nonarchimedean valued field of characteristic p> 0 has at most 2 √ g ( √ g+1) 2 automorphisms. In this note, the unique family of curves which attains this bound, and their automorphism group are determined. 1. ..."
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Cited by 5 (2 self)
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Abstract. It is known that a Mumford curve of genus g / ∈ {5, 6,7, 8} over a nonarchimedean valued field of characteristic p> 0 has at most 2 √ g ( √ g+1) 2 automorphisms. In this note, the unique family of curves which attains this bound, and their automorphism group are determined. 1.
Results 1  10
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326