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]

gollark: (more easily than the weird regex notation of recursive capture groups)
gollark: I'm sure it lets you define functions.
gollark: As planned.
gollark: Although I actually wrote the regex as```pythonWHITESPACE = r"[\t\n ]*"NUMBER = r"\-?(?:0|[1-9][0-9]*)(?:\.[0-9]+)?(?:[eE][+-]?[0-9]+)?"ARRAY = f"(?:\[{WHITESPACE}(?:|(?R)|(?R)(?:,{WHITESPACE}(?R){WHITESPACE})*){WHITESPACE}])"STRING = r'"(?:[^"\\\n]|\\["\\/bfnrt]|\\u[0-9a-fA-F]{4})*"'TERMINAL = f"(?:true|false|null|{NUMBER}|{STRING})"PAIR = f"(?:{WHITESPACE}{STRING}{WHITESPACE}:{WHITESPACE}(?R){WHITESPACE})"OBJECT = f"(?:{{(?:{WHITESPACE}|{PAIR}|(?:{PAIR}(?:,{PAIR})*))}})"VALUE = f"{WHITESPACE}(?:{ARRAY}|{OBJECT}|{TERMINAL}){WHITESPACE}"```which is much easier.
gollark: Regex is kind of like the APL of string pattern matching, in that it's very terse and expressive but incomprehensible.

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


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