A fixed point formula of Lefschetz type in Arakelov geometry IV: the modular height of C.M. abelian varieties

A fixed point formula of Lefschetz type in Arakelov geometry III: representations of Chevalley schemes and heights of flag varieties

We give a new proof of the Jantzen sum formula for integral representations of Chevalley schemes over Spec Z. This is done by applying the fixed point formula of Lefschetz type in Arakelov geometry to generalized flag varieties. Our proof involves the computation of the equivariant Ray-Singer torsion for all equivariant bundles over complex homogeneous spaces. Furthermore, we find several expli...

A Lefschetz Fixed Point Formula for Singular Arithmetic Schemes with Smooth Generic Fibres

In this article, we consider singular equivariant arithmetic schemes whose generic fibres are smooth. For such schemes, we prove a relative fixed point formula of Lefschetz type in the context of Arakelov geometry. This formula is an analog, in the arithmetic case, of the Lefschetz formula proved by R. W. Thomason in [31]. In particular, our result implies a fixed point formula which was conjec...

ar X iv : m at h / 01 05 09 8 v 1 [ m at h . A G ] 1 1 M ay 2 00 1 A fixed point formula of Lefschetz type

This is the second of a series of papers dealing with an analog in Arakelov geometry of the holomorphic Lefschetz fixed point formula. We use the main result [KR2, Th. 4.4] of the first paper to prove a residue formula ”à la Bott” for arithmetic characteristic classes living on arithmetic varieties acted upon by a diagonalisable torus; recent results of BismutGoette on the equivariant (Ray-Sing...

A Hirzebruch proportionality principle in Arakelov geometry

We show that a conjectural extension of a fixed point formula in Arakelov geometry implies results about a tautological subring in the arithmetic Chow ring of bases of abelian schemes. Among the results are an Arakelov version of the Hirzebruch proportionality principle and a formula for a critical power of ĉ1 of the Hodge bundle. 2000 Mathematics Subject Classification: 14G40, 58J52, 20G05, 20...

Common Fixed Point Theorems of Integral Type in Modular Spaces