HIGHER REGULATORS OF SIEGEL SIXFOLDS AND NON-CRITICAL VALUES OF SPIN L-FUNCTIONS
Résumé
We construct classes in the middle degree plus one motivic cohomology of Siegel sixfolds and we compute their image by Beilinson higher regulator in terms of Rankin-Selberg type automorphic integrals. Using results of Pollack and Shah, we relate the integrals to non-critical special values of the degree 8 Spin L-functions. Along the way, by defining and studying complexes of tempered currents on smooth projective complex varieties endowed with a normal crossings divisor, we provide a new description of Deligne-Beilinson cohomology for any Shimura variety. This is particularly useful for computations of higher regulators and fills a gap in the literature on the subject.
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