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Abstract :
[en] In this paper, we introduce the root-Moufang condition and the p-adic Moufang condition. We show that affine buildings of type (A) over tilde(2) satisfying the root-Moufang condition are Bruhat-Tits buildings. Also, every rank 3 affine building satisfying the p-adic Moufang condition is a Bruhat-Tits building. We motivate the introduction of the new conditions by showing that all Bruhat-Tits (A) over tilde(2)-buildings satisfy the root-Moufang condition, and that the (A) over tilde(2)-buildings over a p-adic field also satisfy the p-adic Moufang condition. Another application of the p-adic Moufang condition is given in Part IV of this paper.
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