Determinant groups of Hermitian lattices over local fields. (English) Zbl 1461.11059
Summary: We describe the determinants of the automorphism groups of Hermitian lattices over local fields. Using a result of G. Shimura [Ann. Math. (2) 79, 369–409 (1964; Zbl 0144.29504)], this yields an explicit method to compute the special genera in a given genus of Hermitian lattices over a number field.
MSC:
| 11E39 | Bilinear and Hermitian forms |
| 11E41 | Class numbers of quadratic and Hermitian forms |
| 15A15 | Determinants, permanents, traces, other special matrix functions |
| 15B57 | Hermitian, skew-Hermitian, and related matrices |
Citations:
Zbl 0144.29504References:
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