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.

Kazhdan's theorem

Kazhdan's theorem says the following:

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" by David Kazhdan, Israel J. Math. 44 (1983), no. 2, 139–159.

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. ISSN 0938-0396. Zbl 1079.11002.

See also

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