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Mumford stability in algebraic geometry. (Mumford-Stabilität in der algebraischen Geometrie.) (German) Zbl 0871.14010
Chatterji, S. D. (ed.), Proceedings of the international congress of mathematicians, ICM ’94, August 3-11, 1994, Zürich, Switzerland. Vol. I. Basel: Birkhäuser. 648-655 (1995).
The article provides a very brief but broad review of different contexts where the notion of stability is very useful in the modern algebraic geometry. One context is a stability for vector spaces with a filtration defined only over the extension of the ground field. Certain lemmata about the stability of $$V \otimes W$$ are here of special interest for the author. Then he talks about similar considerations in the field of diophantine approximation and in the studies of Galois modules, $$p$$-adic representation and the structure of crystalline cohomologies. The classical Mumford stability in the geometric invariant theory and its possible refinement for the stacks is briefly mentioned in the introduction.
For the entire collection see [Zbl 0829.00014].

##### MSC:
 14L24 Geometric invariant theory 14F30 $$p$$-adic cohomology, crystalline cohomology