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{\Large Department of Mathematics, BGU}

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{\Huge AGNT}\\[0.2\baselineskip]

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\textbf{On} \emph{Wednesday, December 15, 2021}
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\textbf{At} \emph{16:00 -- 17:15}
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\textbf{In} \emph{-101}

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{\large\scshape Dmitry Kerner 
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  (BGU)
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will talk about
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{\Large\bfseries Finite determinacy of maps. Group orbits vs the tangent spaces\par}
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\textsc{Abstract:}
Consider a morphism of germs of Noetherian schemes, f: (X,x)-\textgreater{} (Y,y). When is it `stable' under perturbations  by higher order terms? I.e. when can such a perturbation be undone by a group action, e.g. by the local coordinate changes. 
This question has been extensively studied for real/complex analytic (or C\^{}k) maps
 (k\^{}n,o)-\textgreater{} (k\^{}m,o). The idea is to reduce the orbit study, Gf, to the study of the tangent space, T\_G f.
The classical methods used vector field integration and infinite dimensional Lie groups, thus obstructing extensions to the zero/positive characteristic. During the last years we have developed a purely algebraic approach to this problem, extending the results to arbitrary characteristic. 
The key tool is the `Lie-type pair'. This is a group G, its would-be tangent space T\_G, and certain maps between G, T\_G, approximating the classical exponential/logarithm.

(joint work with G. Belitskii, A.F. Boix, G.M. Greuel.)








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