Let G be finite group and K a number field or a p-adic field with ring of integers OK . In the first part of the manuscript we present an algorithm that computes the relative algebraic K-group K0(OKâ€¦ (More)

Let E be a number field and G be a finite group. Let A be any OE-order of full rank in the group algebra E[G] and X be a (left) A-lattice. We give a necessary and sufficient condition for X to beâ€¦ (More)

We show that the locally free class group of an order in a semisimple algebra over a number field is isomorphic to a certain ray class group. This description is then used to present an algorithmâ€¦ (More)

Let k be a quadratic imaginary field, p a prime which splits in k/Q and does not divide the class number hk of k. Let L denote a finite abelian extension of k and let K be a subextension of L/k. Inâ€¦ (More)

We develop several algorithms for computations in Galois extensions of p-adic fields. Our algorithms are based on existing algorithms for number fields and are exact in the sense that we do not needâ€¦ (More)

In this paper we will algorithmically prove the global epsilon constant conjecture for all Galois extensions L/Q of degree at most 15. In fact, we will obtain a slightly more general result whoseâ€¦ (More)

In the first part of the talk we describe an algorithm which computes a relative algebraic K-group as an abstract abelian group. We also show how this representation can be used to do computations inâ€¦ (More)

We study the local epsilon constant conjecture as formulated by Breuning in [3]. This conjecture fits into the general framework of the equivariant Tamagawa number conjecture (ETNC) and should beâ€¦ (More)

et E be an elliptic curve defined over a number field k and F a finite cyclic extension of k of p-power degree for an odd prime p. Under certain technical hypotheses, we describe a reinterpretationâ€¦ (More)