Arakelov Intersection Indices of Linear Cycles and the Geometry of Buildings and Symmetric Spaces
نویسنده
چکیده
This paper generalizes Yu. Manin’s approach toward a geometrical interpretation of Arakelov theory at infinity to linear cycles in projective spaces. We show how to interpret certain non-Archimedean Arakelov intersection numbers of linear cycles on Pn−1 with the combinatorial geometry of the Bruhat-Tits building associated to PGL(n). This geometric setting has an Archimedean analogue, namely, the Riemannian symmetric space associated to SL(n,C), which we use to interpret analogous Archimedean intersection numbers of linear cycles in a similar way.
منابع مشابه
Non-archimedean intersection indices on projective spaces and the Bruhat-Tits building for PGL
Inspired by Manin’s approach towards a geometric interpretation of Arakelov theory at infinity, we interpret in this paper non-Archimedean local intersection numbers of linear cycles in Pn−1 with the combinatorial geometry of the Bruhat-Tits building associated to PGL(n).
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