Výsledky vyhledávání - "J. Steffen Müller"

Computing torsion subgroups of Jacobians of hyperelliptic curves of genus 3

Publikováno v: Research in Number Theory, 9(2):23. Springer Nature

We introduce an algorithm to compute the structure of the rational torsion subgroup of the Jacobian of a hyperelliptic curve of genus 3 over the rationals. We apply a implementation of our algorithm to a database of curves with low discriminant due t

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::00f528ea498d46f657a18eadaac6b975
https://doi.org/10.1007/s40993-023-00429-x

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Rational points on X0+(125)

Autor: Vishal Arul, J. Steffen Müller

Publikováno v: Expositiones Mathematicae.

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::8fb5af70921fa4fa1678d8770060b09b
https://doi.org/10.1016/j.exmath.2023.02.009

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Explicit Chabauty--Kim for the Split Cartan Modular Curve of Level 13

Autor: Netan Dogra, J. Steffen Müller, Jennifer S. Balakrishnan, Jan Vonk, Jan Tuitman

Publikováno v: Annals of mathematics, 189(3), 885-944

We extend the explicit quadratic Chabauty methods developed in previous work by the first two authors to the case of non-hyperelliptic curves. This results in a method to compute a finite set of p-adic points, containing the rational points, on a cur

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::1f2624d4d0fe77917c9b2e248cddf6e3
https://research.rug.nl/en/publications/8d0952b9-33c4-4bef-9555-d6ba0e448386

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Explicit quadratic Chabauty over number fields

Autor: Francesca Bianchi, Jennifer S. Balakrishnan, J. Steffen Müller, Amnon Besser

Publikováno v: Israel journal of mathematics, 243

We generalize the explicit quadratic Chabauty techniques for integral points on odd degree hyperelliptic curves and for rational points on genus 2 bielliptic curves to arbitrary number fields using restriction of scalars. This is achieved by combinin

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::9149c8a861d99c2bacbcb05779181715
https://research.rug.nl/en/publications/0c153a3e-09c3-4625-8fff-690669009daf

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The minimal regular model of a Fermat curve of odd squarefree exponent and its dualizing sheaf

Autor: Christian Curilla, J. Steffen Müller

Publikováno v: Kyoto Journal of Mathematics, 60(1), 219-268. Duke University Press
Kyoto J. Math. 60, no. 1 (2020), 219-268

We construct the minimal regular model of the Fermat curve of odd squarefree composite exponent $N$ over the $N$-th cyclotomic integers. As an application, we compute upper and lower bounds for the arithmetic self-intersection of the dualizing sheaf

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::49321414cc15fbcb9c97fa6a2de98565
https://research.rug.nl/en/publications/99101ad0-3820-4a3c-bc91-af5b198dc8b3

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Computing Canonical Heights on Elliptic Curves in Quasi-Linear Time

Autor: J. Steffen Müller, Michael Stoll

We introduce an algorithm that can be used to compute the canonical height of a point on an elliptic curve over the rationals in quasi-linear time. As in most previous algorithms, we decompose the difference between the canonical and the naive height

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::fa1acaefcef7096f68e68819af4103a8
http://arxiv.org/abs/1509.08748

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Canonical heights and division polynomials

Autor: Robin de Jong, J. Steffen Müller

Publikováno v: Mathematical Proceedings of the Cambridge Philosophical Society, 157(2), 357-373

We discuss a new method to compute the canonical height of an algebraic point on a hyperelliptic jacobian over a number field. The method does not require any geometrical models, neither $p$-adic nor complex analytic ones. In the case of genus 2 we a

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::b0e5b4c3247c1adbc06532e2145d6635
http://hdl.handle.net/1887/44011

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Explicit Kummer varieties of hyperelliptic Jacobian threefolds

Autor: J. Steffen Müller

We explicitly construct the Kummer variety associated to the Jacobian of a hyperelliptic curve of genus 3 that is defined over a field of characteristic not equal to 2 and has a Weierstra{\ss} point defined over the same field. We also construct homo

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