Gergely Harcos: A Minkowski-type result for linearly independent subsets of ideal lattices. I

We estimate, in a number field, the maximal number of linearly independent elements with prescribed bounds on their valuations. As a by-product, we obtain new bounds for the successive minima of ideal lattices. Our arguments combine group theory, ramification theory, and the geometry of numbers. This is joint work with Mikołaj Frączyk and Péter Maga.