On many occasions a local object (e.g. the germ of a map at a point) is essentially
\ndetermined (up to a group action) by its finite jet, i.e. its restriction onto some N’th-infinitesimal
\nneighborhood of the point. This “minimalistic stability” is called the Finite Determinacy. It is
\nextremely useful e.g. in deformation theory and in the study of local moduli.
\nFor function germs\/power series the finite determinacy has been classically known. For the
\n(formal\/smooth\/analytic) germs of maps it has been intensively studied since 1960’s.
\nAfter the general introduction I will speak about our recent results. We extend the classical
\ncriteria to the broad class of rings (over a field of zero characteristic) and group actions on
\nfiltered modules. As an application we compute (or give tight bounds to) the orders of determinacy
\nfor numerous scenarios, e.g.: germs of maps, stalks of sheaves\/modules over local rings,
\nquadratic\/skew-symmetric forms.<\/p>\n
Joint work with G. Belitskii.<\/p>\n","protected":false},"excerpt":{"rendered":"
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 N’th-infinitesimal neighborhood of the point. This “minimalistic stability”…
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