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Determinant groups of Hermitian lattices over local fields

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Abstract

We describe the determinants of the automorphism groups of Hermitian lattices over local fields. Using a result of G. Shimura, this yields an explicit method to compute the special genera in a given genus of Hermitian lattices over a number field.

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Acknowledgements

The author would like to thank S. Brandhorst for his valuable comments.

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  1. Lehrstuhl D für Mathematik, RWTH Aachen University, Pontdriesch 14/16, 52062, Aachen, Germany

    Markus Kirschmer

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  1. Markus Kirschmer
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Correspondence to Markus Kirschmer.

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The research is supported by the DFG within the framework of the SFB TRR 195.

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Kirschmer, M. Determinant groups of Hermitian lattices over local fields. Arch. Math. 113, 337–347 (2019). https://doi.org/10.1007/s00013-019-01348-z

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  • DOI: https://doi.org/10.1007/s00013-019-01348-z

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