Event № 1679

On many occasions a local object (e.g. the germ of a map at a point) is essentially determined (up to a group action) by its finite jet, i.e. its restriction onto some Nth-infinitesimal neighborhood of the point. This "minimalistic stability" is called the Finite Determinacy. It is extremely useful e.g. in deformation theory and in the study of local moduli.
For function germs/power series the finite determinacy has been classically known. For the (formal/smooth/analytic) germs of maps it has been intensively studied since the 1960s.
After the general introduction I will speak about our recent results. We extend the classical criteria to the broad class of rings (over a field of zero characteristic) and group actions on filtered modules. As an application we compute (or give tight bounds to) the orders of determinacy for numerous scenarios, e.g.: germs of maps, stalks of sheaves/modules over local rings, quadratic/skew-symmetric forms.
Joint work with G. Belitskii.