Algorithmic proof of the epsilon constant conjecture

摘要

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 whose proof is based on an algorithmic proof of the local epsilon constant conjecture for Galois extensions E/Qp of small degree. To this end we will present an efficient algorithm for the computation of local fundamental classes and address several other problems arising in the algorithmic proof of the local conjecture.