M/E23

The subject of my currently open doctoral thesis is Witt groups of orders, i.e. Noetherian rings of dimension 1, which are subrings of the Dedekind ring. The Dedekind ring is called the maximal order and for it the Witt ring have been well defined. Under the supervision of Prof. Paweł Gładki, we are working on orders that are not maximal - but we are trying to combine the methods used for the Dedekind ring with those used for example by Paul Balmer or Stefan Gille. The short lecture will be about recent results that deal with the natural homomorphism of Witt groups. More or less known examples of injective and non-injective natural homomorphisms will be shown, as well as recent results that were presented, for example, a year ago in Sopron (Hungary) at the 25th Central European Number Theory Conference. Proposed literature: 1. Kazimierz Szymiczek - Witt ring of a commutative ring 2. Marzena Ciemała, Kazimierz Szymiczek - On injectivity of natural homomorphisms of Witt rings 3. Beata Rothkegel - Witt functor of a quadratic order 4. Paweł Gładki, Mateusz Pulikowski - Natural homomorphism of Witt rings of a certain cubic order

Mateusz Pulikowski

Katowice/Dortmund