| Résume | Abstract:
For a degeneration with isolated singularities of a family of smooth and proper varieties in characteristic zero, Milnor's seminal work calculates the difference in Euler characteristics between the generic and special fibres in terms of a sum of certain indices at each singular point. When the singularities are not isolated, a similar formula holds if one replaces Milnor's indices with Fulton's localized intersection numbers. Recently, quadratic refinements of this formula were considered by Levine, Pepin-Lehalleur and Srinivas, where the Euler characteristic is replaced with the motivic Euler characteristic. It remains however unclear what form the formula should take in general. In this talk I will present work in progress with Ran Azouri, Niels Feld, Tasos Moulinos and Simon Pepin Lehalleur establishing a form of the quadratic conductor formula in certain special cases, and proposing a conjectural formula for the case of split semi-stable degenerations.
A key role is played by motivic properties of hermitian K-theory. |
