Periods of Hodge structures and special values of the gamma function

At the end of the 1970s, Gross and Deligne conjectured that periods of geometric Hodge structures with multiplication by an abelian number field are products of values of the gamma function at rational arguments, with exponents determined by the Hodge decomposition. We prove an alternating variant o...

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Bibliographic Details
Published in:Inventiones mathematicae 2017-04, Vol.208 (1), p.247-282
Main Author: Fresan, Javier
Format: Article
Language:English
Subjects:
Algebraic Geometry
Automorphisms
Decomposition
Exponents
Formulas (mathematics)
Gamma function
Joints
Mathematical analysis
Mathematics
Mathematics and Statistics
Multiplication
Number Theory
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Summary:At the end of the 1970s, Gross and Deligne conjectured that periods of geometric Hodge structures with multiplication by an abelian number field are products of values of the gamma function at rational arguments, with exponents determined by the Hodge decomposition. We prove an alternating variant of this conjecture for smooth projective varieties acted upon by an automorphism of finite order, thus improving previous results of Maillot and Rössler. The proof relies on a product formula for periods of regular singular connections due to Saito and Terasoma.
ISSN:0020-9910
1432-1297
DOI:10.1007/s00222-016-0690-4