# Determinant groups of hermitian lattices over local fields

## TL;DR

This paper provides a method to compute special genera of hermitian lattices over number fields by analyzing determinants of automorphism groups over local fields, leveraging Shimura's results.

## Contribution

It introduces an explicit approach to determine determinants of automorphism groups of hermitian lattices over local fields, aiding in classifying their special genera.

## Key findings

- Explicit method for computing determinants of automorphism groups
- Application of Shimura's result to classify hermitian lattices
- Enhanced understanding of the structure of hermitian lattices over local fields

## 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.