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Transactions of the American Mathematical Society, ISSN 0002-9947, 02/2019, Volume 371, Issue 2, pp. 1119 - 1149
We give an explicit description of fundamental domains associated with the p-adic uniformisation of families of Shimura curves of discriminant Dp and level N... 
Shimura curves | Mumford curves | p-adic fundamental domains | MATHEMATICS | UNIFORMIZATION | CONSTRUCTION | POINTS
Journal Article
Journal of Symbolic Computation, ISSN 0747-7171, 05/2015, Volume 68, Issue 2, pp. 259 - 284
Mumford showed that Schottky subgroups of PGL(2,K) give rise to certain curves, now called Mumford curves, over a non-archimedean field K... 
Tropical geometry | Mumford curve | MATHEMATICS, APPLIED | COMPUTER SCIENCE, THEORY & METHODS | ANALYTIC CONSTRUCTION | Algorithms
Journal Article
Duke Mathematical Journal, ISSN 0012-7094, 2016, Volume 165, Issue 16, pp. 3189 - 3240
Let X be a curve of genus g >= 2 over a number field F of degree d = [F : Q]. The conjectural existence of a uniform bound N(g, d) on the number #X(F... 
MATHEMATICS | REDUCTION | CHABAUTY | GEOMETRY
Journal Article
Compositio mathematica, ISSN 0010-437X, 11/2015, Volume 151, Issue 11, pp. 2076 - 2130
Journal Article
Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry, ISSN 0138-4821, 3/2017, Volume 58, Issue 1, pp. 47 - 67
In the present paper, we investigate the question if the skeleton of a Mumford curve of genus two can be tropicalized faithfully in dimension three, i.e... 
Geometry | Algebra | Berkovich spaces | Convex and Discrete Geometry | Tropicalization | Tropical geometry | Algebraic Geometry | 14H30 | Mathematics | Mumford curves | 14T05 | 14H45
Journal Article
Kodai mathematical journal, ISSN 0386-5991, 2018, Volume 41, Issue 2, pp. 240 - 263
... of the projective line by Mumford curves over complete discrete valuation fields of positive characteristic p... 
cyclic covering | Mumford curve | rigid analytic geometry | Rigid analytic geometry | Cyclic covering | MATHEMATICS
Journal Article
Journal of Algebra, ISSN 0021-8693, 01/2014, Volume 397, pp. 47 - 67
Journal Article
Journal of Algebra, ISSN 0021-8693, 12/2012, Volume 372, pp. 584 - 594
In this paper, we are interested in the generic initial ideals of singular projective curves with respect to the graded lexicographic order... 
Castelnuovo–Mumford regularity | Partial elimination ideal | Graded lexicographic order | Generic initial ideal | Singular projective curve | THREEFOLDS | MATHEMATICS | Castelnuovo-Mumford regularity | CODIMENSION 2 | DEGREE-COMPLEXITY | SMOOTH SURFACES | Generic drugs
Journal Article
Publications of the Research Institute for Mathematical Sciences, ISSN 0034-5318, 06/2010, Volume 46, Issue 2, pp. 219 - 253
We construct a rigid analytical regulator for the K-2 of Mumford curves, a non-archimedean analogue of th9e complex analytical Beilinson-Bloch-Deligne regulator. 
MATHEMATICS | regulator | Mumford curves
Journal Article
Bulletin of the American Mathematical Society, ISSN 0273-0979, 04/2020, Volume 57, Issue 2, pp. 171 - 267
Journal Article
Annals of mathematics, ISSN 0003-486X, 5/2020, Volume 191, Issue 3, pp. 949 - 1001
...). We apply this strategy to prove a conjecture of Bogomolov, Fu, and Tschinkel asserting uniform bounds on the number of common torsion points of elliptic curves in the case of two Legendre curves over ℂ... 
torsion points | MATHEMATICS | arithmetic intersection | EQUIDISTRIBUTION | Manin-Mumford | Lattes maps | VARIETIES | preperiodic points | CANONICAL HEIGHTS | elliptic curves | non-archimedean potential theory
Journal Article
Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg, ISSN 0025-5858, 4/2013, Volume 83, Issue 1, pp. 83 - 99
Journal Article
Journal of Algebra, ISSN 0021-8693, 01/2019, Volume 517, pp. 119 - 166
... is a curve of genus 0. As abstract group Γ is an amalgam of a finite tree of finite groups... 
Rigid geometry | Mumford groups | Discontinuous groups | Stratified bundles | Mumford curves | Amalgams | Orbifolds | MAXIMAL AUTOMORPHISM GROUP | SUBGROUPS | PGL(K) | To be checked by Faculty | MATHEMATICS
Journal Article
Communications in algebra, ISSN 0092-7872, 09/2020, Volume 48, Issue 9, pp. 3724 - 3742
In this paper we explicitly describe the symbolic powers of the ideal defining the curve in parametrized by where q, m are positive integers, and We show that the symbolic blowup algebra is Noetherian and Gorenstein... 
1305 | symbolic Rees algebra | resurgence | Waldschmidt constant | Primary: 13A30 | Castelnuovo-Mumford regularity | MATHEMATICS | RESURGENCES | POWERS | IDEALS | ASYMPTOTIC-BEHAVIOR
Journal Article
Transactions of the American Mathematical Society, ISSN 0002-9947, 01/2006, Volume 358, Issue 1, pp. 267 - 284
In this paper we prove that the regularity of a connected curve is bounded by its degree minus its codimension plus 1... 
Conic sections | Algebra | Mathematical theorems | Hyperplanes | Secant function | Secant lines | Curves | Connected curves | Castelnuovo-Mumford regularity | Eisenbud-Goto conjecture | THREEFOLDS | MATHEMATICS | GENERIC PROJECTIONS | SMOOTH SURFACES | connected curves
Journal Article
Publications of the Research Institute for Mathematical Sciences, ISSN 0034-5318, 2010, Volume 46, Issue 2, pp. 219 - 253
Journal Article
Journal of Number Theory, ISSN 0022-314X, 06/2018, Volume 187, pp. 344 - 371
We calculate the tropical Dolbeault cohomology for the analytifications of P1 and Mumford curves over non-archimedean fields... 
Non-archimedean curves | Poincaré duality | Berkovich spaces | Smooth differential forms on Berkovich spaces | Mumford curves | Non-archimedean geometry | Tropicalizations | MATHEMATICS | Poincare duality | Smooth differential forms on
Journal Article
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