The spinor class field for a genus of orders of maximal rank in a quaternion algebra 𝔄 over a
number field K is an abelian extension Σ/K provided with a distance function associating …

We study a form of refined class number formula (resp. type number formula) for maximal
orders in totally definite quaternion algebras over real quadratic fields, by taking into …

We give a deterministic polynomial time algorithm to compute the endomorphism ring of a
supersingular elliptic curve in characteristic p, provided that we are given two noncommuting …

We explicitly compute the largest subtree, in the local Bruhat–Tits tree for PSL 2 (k), whose
vertices correspond to maximal orders containing a fixed order generated by a pair of …

Bolytropes are bounded subsets of an affine building that consist of all points that have
distance at most r from some polytrope. We prove that the points of a bolytrope describe the …

This dissertation considers two problems regarding the structure of isogenies between
supersingular elliptic curves which are motivated by isogeny-based cryptography. The first …

We describe the set of maximal orders in a 2-by-2 matrix algebra over a non-commutative
local division algebra B containing a given suborder, for certain important families of such …

Similar to the field of real numbers R, which can be constructed as the completion of the
rational numbers with respect the usual absolute value|·|, the field of p-adic numbers Q_p is …

Bolytropes are bounded subsets of an affine building that consist of all points that have
distance at most $ r $ from some polytrope. We prove that the points of a bolytrope describe …

It goes without saying that some of the most important roles in the developments of number
theory during the last century were played by modular forms and modular curves, which are …