Computing residue class rings and Picard groups of orders

DOI10.1016/j.jalgebra.2005.04.013zbMath1094.11046OpenAlexW2018372389MaRDI QIDQ2577535

Jürgen Klüners, Sebastian Pauli

Publication date: 22 December 2005

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jalgebra.2005.04.013

zbMATH Keywords

Picard groupsorders of global fieldsunits of residue class rings

Mathematics Subject Classification ID

Units and factorization (11R27) Algebraic number theory computations (11Y40) Class groups and Picard groups of orders (11R65)

Related Items (12)

Computing generators of the unit group of an integral Abelian group ring. ⋮ On the restricted Hilbert-Speiser and Leopoldt properties ⋮ Extensions and torsors for finite group schemes ⋮ Computing the endomorphism ring of an ordinary abelian surface over a finite field ⋮ Finite subgroups of automorphisms of K3 surfaces ⋮ Isomorphism classes of Drinfeld modules over finite fields ⋮ Ideal classes of orders in quaternion algebras ⋮ Fast heuristic algorithms for computing relations in the class group of a quadratic order, with applications to isogeny evaluation ⋮ Computing the ideal class monoid of an order ⋮ An 𝐿(1/3) algorithm for ideal class group and regulator computation in certain number fields ⋮ Computing abelian varieties over finite fields isogenous to a power ⋮ An algorithm for the principal ideal problem in indefinite quaternion algebras

Uses Software

• KANT/KASH
• Magma

Cites Work

• KANT V4
• Computing Riemann-Roch spaces in algebraic function fields and related topics.
• Computing the multiplicative group of residue class rings
• Advanced Topics in Computional Number Theory
• Picard Groups and Refined Discrete Logarithms
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