Thursday 24 October 2024 at 2 pm, as part of the Al@Bicocca seminar cycle, Kristýna Zemková (University of Victoria) will talk about
Title: Equivalence relations of quadratic forms in characteristic two
Abstract: It is well-known that quadratic forms can be diagonalized over fields and that they are in a one-to-one correspondence with bilinear forms; the algebraic theory of quadratic forms is built on these two properties. But there is a catch – division by two is required. Over a field of characteristic 2, neither of the two properties holds, and the whole quadratic form theory needs to be rebuilt from scratch. The equivalence relations of quadratic forms that are usually studied and compared are: similarity (two quadratic forms only differ by a scalar multiple), birational equivalence (the corresponding quadrics are birationally equivalent), stable birational equivalence (the corresponding quadrics are stably birationally equivalent), and motivic equivalence (we skip the explanation). In the talk, we dive into the parallel universe of quadratic forms in characteristic 2. After a brief introduction, I will focus on the equivalence relations of quadratic forms, and the development of the results in the last five years. Instead of motivic equivalence, which is unavailable in our universe, we define Vishik equivalence: a purely algebraic analogue of motivic equivalence. The main question of the talk will be: Are Vishik equivalent quadratic forms always similar? (Spoiler: It depends.)
Information to attend
The seminar will be held in Room 3014 (3rd Floor) - U5 Building, University of Milan-Bicocca and will also be available online at the following Webex link