Arithmetic variety

In mathematics, an arithmetic variety is the quotient space of a Hermitian symmetric space by an arithmetic subgroup of the associated algebraic Lie group.

## Contents

* 1 Kazhdan's theorem
* 2 References
* 3 Further reading
* 4 See also

## Kazhdan's theorem

Kazhdan's theorem says the following:

Kazhdan's theorem -- If X is an arithmetic variety, then, for all automorphisms σ of the complex numbers, σX is also an arithmetic variety.[1]

## References

1. ↑ "On arithmetic varieties II". Israel Journal of Mathematics 44 (2): 139–159. 1983. doi:10.1007/BF02760617.

## Further reading

* Manin, Yu. I.; Panchishkin, A. A. (2007). Introduction to Modern Number Theory. Encyclopaedia of Mathematical Sciences. 49 (Second ed.). ISBN 978-3-540-20364-3.

## See also

* Arithmetic Chow groups
* Arithmetic of abelian varieties
* Abelian variety

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