具有非离散赋值的广义多边形定义的二维仿射R-建筑
Two-dimensional affine R-buildings defined by generalized polygons with non-discrete valuation
摘要：
本文完成了作者在前一篇文章中开始的关于A~ 2型和C~ 2型非离散R-建筑分别与射影平面和具有非离散赋值的广义四边形的“等价性”的证明。我们还完成了证明的“等价性”的仿射建设的秩3与广义多边形的离散赋值（通过证明这一广义六边形）。我们还补充了第二作者的结果，证明了唯一性的标量倍的重量序列的多边形与非离散赋值。作为应用，我们给出了一些新的显式定义的非离散R-建筑物，特别是一类具有任意剩余的A_2型建筑物.
英文摘要：
In this paper we complete the proof of the "equivalence" of non-discrete R-buildings of types A~_2 and C~_2, with, respectively, projective planes and generalized quadrangles with non-discrete valuation, begun in previous paper of the authors. We also complete the proof of the "equivalence" of an affine building of rank 3 with a generalized polygon with discrete valuation (by proving this for generalized hexagons). We also complement a result of the second author by proving uniqueness up to scalar multiples of the weight sequences of polygons with non-discrete valuation. As an application, we produce some new explicitly defined non-discrete R-buildings, in particular a class of type A~_2 with arbitrary residues.
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