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:

{{math theorem|name=Kazhdan's theorem|note=|style=|math_statement= If X is an arithmetic variety, then, for all automorphisms σ of the complex numbers, σX is also an arithmetic variety.<ref>{{cite journal | title=On arithmetic varieties II | first1=David | last1=Kazhdan | authorlink1=David Kazhdan | journal=Israel Journal of Mathematics | volume=44 | year=1983 | issue=2 | pages=139–159 | doi=10.1007/BF02760617 | doi-access=free}}</ref> }}

==References== {{reflist}} ==Further reading== *{{cite book | first1=Yu. I. | last1=Manin | authorlink1=Yuri I. Manin | first2=A. A. | last2=Panchishkin | title=Introduction to Modern Number Theory | series=Encyclopaedia of Mathematical Sciences | volume=49 | edition=Second | year=2007 | isbn=978-3-540-20364-3 | issn=0938-0396 | zbl=1079.11002 }}

==See also== *Arithmetic Chow groups *Arithmetic of abelian varieties *Abelian variety

Category:Arithmetic geometry

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