Abstract
We study the compatibility of Manin’s conjecture with natural geometric constructions, like fibrations induced from torsors under linear algebraic groups. The main problem it to understand the variation of metrics from fiber to fiber. For this we introduce the notions of “arithmetic torsors”, “adelic torsion” and “Arakelov L-functions”. We discuss concrete examples, like horospherical varieties and equivariant compactifications of semiabelian varieties. These techniques are applied to prove “going up” and “descent” theorems for height zeta functions on such fibrations.
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© 2001 Birkhäusr Verlag, P.O.Box 133, CH-4010 Basel, Switzerland
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Chambert-Loir, A., Tschinkel, Y. (2001). Torseurs Arithmétiques Et Espaces Fibres. In: Peyre, E., Tschinkel, Y. (eds) Rational Points on Algebraic Varieties. Progress in Mathematics, vol 199. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8368-9_3
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DOI: https://doi.org/10.1007/978-3-0348-8368-9_3
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