15 citations · 17 across the 9 of their papers we have counts for
10 papers
On hyperbolic lattices whose reduced automorphism group is virtually abelian
Simon Brandhorst, Markus Kirschmer, Giacomo Mezzedimi
We give a classification of even integral lattices with virtually abelian reduced automorphism group. As a consequence, we complete the classification of K3 surfaces with virtually…
Enumerating orders in number fields
Markus Kirschmer, Jürgen Klüners
We arrange the orders in an algebraic number field in a tree. This tree can be used to enumerate all orders of bounded index in the maximal order as well as the orders over some gi…
Chow groups of one-dimensional noetherian domains
Markus Kirschmer, Jürgen Klüners
We discuss various connections between ideal classes, divisors, Picard and Chow groups of one-dimensional noetherian domains. As a result of these, we give a method to compute Chow…
Spanning the isogeny class of a power of an ordinary elliptic curve over a finite field. Application to the number of rational points of curves of genus
Markus Kirschmer, Fabien Narbonne, Christophe Ritzenthaler +1
Let be an ordinary elliptic curve over a finite field and be a positive integer. Under some technical assumptions, we give an algorithm to span the isomorphism classes of p…
Determinant groups of hermitian lattices over local fields
Markus Kirschmer
We describe the determinants of the automorphism groups of hermitian lattices over local fields. Using a result of G. Shimura, this yields an explicit method to compute the special…
Quaternary quadratic lattices over number fields
Markus Kirschmer, Gabriele Nebe
We relate proper isometry classes of maximal lattices in a totally definite quaternary quadratic space (V,q) with trivial discriminant to certain equivalence classes of ideals in t…
One class genera of lattice chains over number fields
Markus Kirschmer, Gabriele Nebe
We classify all one-class genera of admissible lattice chains of length at least 2 in hermitian spaces over number fields.
Single-Class Genera of Positive Integral Lattices
David Lorch, Markus Kirschmer
We give an enumeration of all positive definite primitive Z-lattices in dimension >= 3 whose genus consists of a single isometry class. This is achieved by using bounds obtained fr…
Finite symplectic matrix groups
Markus Kirschmer
This paper classifies the maximal finite subgroups of Sp(2n,Q) for 1 <= n <= 11 up to conjugacy in GL(2n,Q).
Algorithmic enumeration of ideal classes for quaternion orders
Markus Kirschmer, John Voight
We provide algorithms to count and enumerate representatives of the (right) ideal classes of an Eichler order in a quaternion algebra defined over a number field. We analyze the ru…