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- ItemCocharacter-closure and spherical buildings(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2015) Bate, Michael; Herpel, Sebastian; Benjamin, Martin; Röhrle, GerhardLet k be a field, let G be a reductive k-group and V an affine k-variety on which G acts. In this note we continue our study of the notion of cocharacter-closed G(k)-orbits in V . In earlier work we used a rationality condition on the point stabilizer of a G-orbit to prove Galois ascent/descent and Levi ascent/descent results concerning cocharacter-closure for the corresponding G(k)-orbit in V . In the present paper we employ building-theoretic techniques to derive analogous results.