{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,12]],"date-time":"2026-06-12T18:00:00Z","timestamp":1781287200221,"version":"3.54.1"},"reference-count":31,"publisher":"American Mathematical Society (AMS)","issue":"361","license":[{"start":{"date-parts":[[2026,6,24]],"date-time":"2026-06-24T00:00:00Z","timestamp":1782259200000},"content-version":"am","delay-in-days":365,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>\n                    Given a superelliptic curve\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper Y Subscript upper K Baseline colon y Superscript n Baseline equals f left-parenthesis x right-parenthesis\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:msub>\n                              <mml:mi>Y<\/mml:mi>\n                              <mml:mi>K<\/mml:mi>\n                            <\/mml:msub>\n                            <mml:mo>:<\/mml:mo>\n                            <mml:mspace width=\"thickmathspace\"\/>\n                            <mml:msup>\n                              <mml:mi>y<\/mml:mi>\n                              <mml:mi>n<\/mml:mi>\n                            <\/mml:msup>\n                            <mml:mo>=<\/mml:mo>\n                            <mml:mi>f<\/mml:mi>\n                            <mml:mo stretchy=\"false\">(<\/mml:mo>\n                            <mml:mi>x<\/mml:mi>\n                            <mml:mo stretchy=\"false\">)<\/mml:mo>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">Y_K:\\; y^n=f(x)<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    over a local field\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper K\">\n                        <mml:semantics>\n                          <mml:mi>K<\/mml:mi>\n                          <mml:annotation encoding=\"application\/x-tex\">K<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    , we describe the theoretical background and an implementation of a new algorithm for computing the\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"German o Subscript upper K\">\n                        <mml:semantics>\n                          <mml:msub>\n                            <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                              <mml:mi mathvariant=\"fraktur\">o<\/mml:mi>\n                            <\/mml:mrow>\n                            <mml:mi>K<\/mml:mi>\n                          <\/mml:msub>\n                          <mml:annotation encoding=\"application\/x-tex\">\\mathfrak {o}_K<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    -lattice of integral differential forms on\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper Y Subscript upper K\">\n                        <mml:semantics>\n                          <mml:msub>\n                            <mml:mi>Y<\/mml:mi>\n                            <mml:mi>K<\/mml:mi>\n                          <\/mml:msub>\n                          <mml:annotation encoding=\"application\/x-tex\">Y_K<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    . We build on the results of Obus and Wewers [J. Algebraic Geom. 29 (2020), pp.\u00a0691\u2013728] who describe arbitrary regular models of the projective line using only valuations. One novelty of our approach is that we construct an\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"German o Subscript upper K\">\n                        <mml:semantics>\n                          <mml:msub>\n                            <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                              <mml:mi mathvariant=\"fraktur\">o<\/mml:mi>\n                            <\/mml:mrow>\n                            <mml:mi>K<\/mml:mi>\n                          <\/mml:msub>\n                          <mml:annotation encoding=\"application\/x-tex\">\\mathfrak {o}_K<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    -model of\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper Y Subscript upper K\">\n                        <mml:semantics>\n                          <mml:msub>\n                            <mml:mi>Y<\/mml:mi>\n                            <mml:mi>K<\/mml:mi>\n                          <\/mml:msub>\n                          <mml:annotation encoding=\"application\/x-tex\">Y_K<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    with only rational singularities, but which may not be regular.\n                  <\/p>","DOI":"10.1090\/mcom\/4115","type":"journal-article","created":{"date-parts":[[2025,6,24]],"date-time":"2025-06-24T11:58:41Z","timestamp":1750766321000},"page":"2559-2593","source":"Crossref","is-referenced-by-count":0,"title":["Integral differential forms for superelliptic curves"],"prefix":"10.1090","volume":"95","author":[{"given":"Sabrina","family":"Kunzweiler","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Stefan","family":"Wewers","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"14","published-online":{"date-parts":[[2025,6,24]]},"reference":[{"key":"1","series-title":"Mathematical Surveys and Monographs","isbn-type":"print","doi-asserted-by":"publisher","DOI":"10.1090\/surv\/033","volume-title":"Spectral theory and analytic geometry over non-Archimedean fields","volume":"33","author":"Berkovich, Vladimir G.","year":"1990","ISBN":"https:\/\/id.crossref.org\/isbn\/0821815342"},{"issue":"3-4","key":"2","doi-asserted-by":"publisher","first-page":"235","DOI":"10.1006\/jsco.1996.0125","article-title":"The Magma algebra system. I. The user language","volume":"24","author":"Bosma, Wieb","year":"1997","journal-title":"J. Symbolic Comput.","ISSN":"https:\/\/id.crossref.org\/issn\/0747-7171","issn-type":"print"},{"issue":"1","key":"3","doi-asserted-by":"publisher","first-page":"65","DOI":"10.1007\/BF01405091","article-title":"Singularit\u00e9s rationnelles et quotients par les groupes r\u00e9ductifs","volume":"88","author":"Boutot, Jean-Fran\u00e7ois","year":"1987","journal-title":"Invent. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0020-9910","issn-type":"print"},{"key":"4","isbn-type":"print","doi-asserted-by":"publisher","first-page":"115","DOI":"10.1007\/978-3-030-77700-5_4","article-title":"Reduction types of genus-3 curves in a special stratum of their moduli space","author":"Bouw, Irene","year":"[2021] \\copyright2021","ISBN":"https:\/\/id.crossref.org\/isbn\/9783030776992"},{"key":"5","unstructured":"T. Dokchitser, Models of curves, \\nolinkurl{https:\/\/people.maths.bris.ac.uk\/ matyd\/newton\/}."},{"issue":"11","key":"6","doi-asserted-by":"publisher","first-page":"2519","DOI":"10.1215\/00127094-2020-0079","article-title":"Models of curves over discrete valuation rings","volume":"170","author":"Dokchitser, Tim","year":"2021","journal-title":"Duke Math. J.","ISSN":"https:\/\/id.crossref.org\/issn\/0012-7094","issn-type":"print"},{"issue":"3-4","key":"7","doi-asserted-by":"publisher","first-page":"1213","DOI":"10.1007\/s00208-021-02319-y","article-title":"Arithmetic of hyperelliptic curves over local fields","volume":"385","author":"Dokchitser, Tim","year":"2023","journal-title":"Math. Ann.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5831","issn-type":"print"},{"key":"8","doi-asserted-by":"publisher","first-page":"30","DOI":"10.1016\/j.jalgebra.2014.12.022","article-title":"Residual ideals of MacLane valuations","volume":"427","author":"Fern\u00e1ndez, Julio","year":"2015","journal-title":"J. Algebra","ISSN":"https:\/\/id.crossref.org\/issn\/0021-8693","issn-type":"print"},{"issue":"236","key":"9","doi-asserted-by":"publisher","first-page":"1675","DOI":"10.1090\/S0025-5718-01-01320-5","article-title":"Empirical evidence for the Birch and Swinnerton-Dyer conjectures for modular Jacobians of genus 2 curves","volume":"70","author":"Flynn, E. Victor","year":"2001","journal-title":"Math. Comp.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5718","issn-type":"print"},{"key":"10","series-title":"Lecture Notes in Mathematics, Vol. 208","volume-title":"The tame fundamental group of a formal neighbourhood of a divisor with normal crossings on a scheme","author":"Grothendieck, Alexander","year":"1971"},{"key":"11","series-title":"Lecture Notes in Mathematics","isbn-type":"print","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-26638-1","volume-title":"N\\'{e}ron models and base change","volume":"2156","author":"Halle, Lars Halvard","year":"2016","ISBN":"https:\/\/id.crossref.org\/isbn\/9783319266374"},{"issue":"5","key":"12","doi-asserted-by":"publisher","first-page":"1073","DOI":"10.2307\/2374941","article-title":"Toric singularities","volume":"116","author":"Kato, Kazuya","year":"1994","journal-title":"Amer. J. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0002-9327","issn-type":"print"},{"issue":"1","key":"13","doi-asserted-by":"publisher","first-page":"37","DOI":"10.1023\/A:1000580901251","article-title":"A discriminant and an upper bound for \ud835\udf14\u00b2 for hyperelliptic arithmetic surfaces","volume":"115","author":"Kausz, Ivan","year":"1999","journal-title":"Compositio Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0010-437X","issn-type":"print"},{"issue":"2","key":"14","doi-asserted-by":"publisher","first-page":"Paper No. 25, 17","DOI":"10.1007\/s40993-020-00200-6","article-title":"Differential forms on hyperelliptic curves with semistable reduction","volume":"6","author":"Kunzweiler, Sabrina","year":"2020","journal-title":"Res. Number Theory","ISSN":"https:\/\/id.crossref.org\/issn\/2522-0160","issn-type":"print"},{"key":"15","unstructured":"S. Kunzweiler, Models of curves and integral differential forms, Ph.D. Thesis, Universit\u00e4t Ulm, 2021."},{"key":"16","unstructured":"S. Kunzweiler and S. Wewers, \\url{https:\/\/github.com\/swewers\/regular_models}."},{"issue":"36","key":"17","doi-asserted-by":"crossref","first-page":"195","DOI":"10.1007\/BF02684604","article-title":"Rational singularities, with applications to algebraic surfaces and unique factorization","author":"Lipman, Joseph","year":"1969","journal-title":"Inst. Hautes \\'{E}tudes Sci. Publ. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0073-8301","issn-type":"print"},{"issue":"1","key":"18","doi-asserted-by":"publisher","first-page":"151","DOI":"10.2307\/1971141","article-title":"Desingularization of two-dimensional schemes","volume":"107","author":"Lipman, Joseph","year":"1978","journal-title":"Ann. of Math. (2)","ISSN":"https:\/\/id.crossref.org\/issn\/0003-486X","issn-type":"print"},{"key":"19","series-title":"Oxford Graduate Texts in Mathematics","isbn-type":"print","volume-title":"Algebraic geometry and arithmetic curves","volume":"6","author":"Liu, Qing","year":"2002","ISBN":"https:\/\/id.crossref.org\/isbn\/0198502842"},{"issue":"3","key":"20","doi-asserted-by":"publisher","first-page":"363","DOI":"10.2307\/1989629","article-title":"A construction for absolute values in polynomial rings","volume":"40","author":"MacLane, Saunders","year":"1936","journal-title":"Trans. Amer. Math. Soc.","ISSN":"https:\/\/id.crossref.org\/issn\/0002-9947","issn-type":"print"},{"key":"21","series-title":"Cambridge Studies in Advanced Mathematics","isbn-type":"print","volume-title":"Commutative ring theory","volume":"8","author":"Matsumura, Hideyuki","year":"1989","ISBN":"https:\/\/id.crossref.org\/isbn\/0521367646","edition":"2"},{"key":"22","first-page":"575","article-title":"An explicit approach to residues on and dualizing sheaves of arithmetic surfaces","volume":"16","author":"Morrow, Matthew","year":"2010","journal-title":"New York J. Math."},{"issue":"2","key":"23","doi-asserted-by":"publisher","first-page":"382","DOI":"10.1017\/S001708952400003X","article-title":"Models and integral differentials of hyperelliptic curves","volume":"66","author":"Muselli, Simone","year":"2024","journal-title":"Glasg. Math. J.","ISSN":"https:\/\/id.crossref.org\/issn\/0017-0895","issn-type":"print"},{"key":"24","isbn-type":"print","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-37663-7","volume-title":"Algebraische Zahlentheorie","author":"Neukirch, J\u00fcrgen","year":"1992","ISBN":"https:\/\/id.crossref.org\/isbn\/3540542736"},{"issue":"2","key":"25","doi-asserted-by":"publisher","first-page":"Paper No. 27, 27","DOI":"10.1007\/s40993-022-00323-y","article-title":"Explicit minimal embedded resolutions of divisors on models of the projective line","volume":"8","author":"Obus, Andrew","year":"2022","journal-title":"Res. Number Theory","ISSN":"https:\/\/id.crossref.org\/issn\/2522-0160","issn-type":"print"},{"key":"26","doi-asserted-by":"crossref","unstructured":"A. Obus and P. Srinivasan, Conductor-discriminant inequality for hyperelliptic curves in odd residue characteristic, Int. Math. Res. Not. IMRN 2024 (2024), no. 9, 7343\u20137359.","DOI":"10.1093\/imrn\/rnad173"},{"issue":"4","key":"27","doi-asserted-by":"publisher","first-page":"691","DOI":"10.1090\/jag\/745","article-title":"Explicit resolution of weak wild quotient singularities on arithmetic surfaces","volume":"29","author":"Obus, Andrew","year":"2020","journal-title":"J. Algebraic Geom.","ISSN":"https:\/\/id.crossref.org\/issn\/1056-3911","issn-type":"print"},{"key":"28","unstructured":"J. R\u00fcth, Models of curves and valuations, Ph.D. Thesis, Universit\u00e4t Ulm, 2015."},{"key":"29","unstructured":"J. R\u00fcth and S. Wewers, MCLF: a Sage toolbox for computations with models of curves over local fields, \\url{https:\/\/github.com\/MCLF\/mclf}."},{"key":"30","unstructured":"The Sage Developers, Sagemath, the Sage mathematics software system (version 10.5), 2025, \\url{https:\/\/www.sagemath.org}."},{"issue":"1","key":"31","doi-asserted-by":"publisher","first-page":"138","DOI":"10.1080\/10586458.2019.1592035","article-title":"Numerical verification of the Birch and Swinnerton-Dyer conjecture for hyperelliptic curves of higher genus over \u211a up to squares","volume":"31","author":"van Bommel, Raymond","year":"2022","journal-title":"Exp. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/1058-6458","issn-type":"print"}],"container-title":["Mathematics of Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.ams.org\/mcom\/2026-95-361\/S0025-5718-2025-04115-2\/S0025-5718-2025-04115-2.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,6,12]],"date-time":"2026-06-12T17:54:17Z","timestamp":1781286857000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.ams.org\/mcom\/2026-95-361\/S0025-5718-2025-04115-2\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,6,24]]},"references-count":31,"journal-issue":{"issue":"361","published-print":{"date-parts":[[2026,9]]}},"alternative-id":["S0025-5718-2025-04115-2"],"URL":"https:\/\/doi.org\/10.1090\/mcom\/4115","archive":["CLOCKSS","Portico"],"relation":{},"ISSN":["1088-6842","0025-5718"],"issn-type":[{"value":"1088-6842","type":"electronic"},{"value":"0025-5718","type":"print"}],"subject":[],"published":{"date-parts":[[2025,6,24]]}}}