Strong approximation for Zariski dense subgroups over arbitrary global fields
نویسندگان
چکیده
منابع مشابه
Zariski dense surface subgroups in SL(4,Z)
The result of [6] is the existence of an infinite family of Zariski dense surface subgroups of fixed genus inside SL(3,Z); here we exhibit such subgroups inside SL(4,Z) and symplectic groups. In this setting the power of such a result comes in large part from the conclusion that the groups are Zariski dense the existence of surface groups inside SL(4,Z) can be proved fairly easily, since it’s n...
متن کاملZariski dense surface subgroups in SL(3,Z)
The nature of finitely generated infinite index subgroups of SL(3,Z) remains extremely mysterious. It follows from the famous theorem of Tits [12] that free groups abound and, moreover, Zariski dense free groups abound. Less trivially, classical arithmetic considerations (see for example §6.1 of [9]) can be used to construct surface subgroups of SL(3,Z) of every genus ≥ 2. However these are con...
متن کاملMultiplication over Arbitrary Fields
We prove a lower bound of 52n2 3n for the rank of n n–matrix multiplication over an arbitrary field. Similar bounds hold for the rank of the multiplication in noncommutative division algebras and for the multiplication of upper triangular matrices.
متن کاملInvariant Measures for Algebraic Actions, Zariski Dense Subgroups and Kazhdan’s Property (t )
Let k be any locally compact non-discrete field. We show that finite invariant measures for k-algebraic actions are obtained only via actions of compact groups. This extends both Borel’s density and fixed point theorems over local fields (for semisimple/solvable groups, resp.). We then prove that for k-algebraic actions, finitely additive finite invariant measures are obtained only via actions ...
متن کاملBers Slices Are Zariski Dense
Each Bers slice is a holomorphically embedded copy of Teichmüller space within XC(S). While it follows that BY can be locally described as the common zero locus of finitely many analytic functions on XC(S), it is known that the Bers slice is not a locally algebraic set [DK]—this is used to show that W. Thurston’s skinning map is not a constant function [DK]. We prove a stronger result about the...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Commentarii Mathematici Helvetici
سال: 2000
ISSN: 0010-2571,1420-8946
DOI: 10.1007/s000140050142