#### DOCUMENTA MATHEMATICA,
Vol. Extra Volume: Alexander S. Merkurjev's Sixtieth Birthday (2015), 513-528

** Vladimir L. Popov **
Around the Abhyankar--Sathaye Conjecture

A «rational» version of the strengthened form of the Commuting Derivation
Conjecture, in which the assumption of commutativity is dropped, is proved.
A systematic method of constructing in any dimension greater than $3$ the
examples answering in the negative a question by M. El Kahoui is developed.

2010 Mathematics Subject Classification: Primary 14R10; Secondary 14R20, 14L30, 20G15.

Keywords and Phrases: Coordinate, locally nilpotent derivation, affine algebraic group, action,
orbit.

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