ON GENERATORS OF ARITHMETIC GROUPS OVER FUNCTION FIELDS
نویسندگان
چکیده
منابع مشابه
On Generators of Arithmetic Groups over Function Fields
Fq = the finite field with q elements; throughout the paper q is assumed to be odd. A = Fq[T ], T indeterminate. F = Fq(T ) = the fraction field of A. |F | = the set of places of F . For x ∈ |F |, Fx = the completion of F at x. Ox = {z ∈ Fx | ordx(z) ≥ 0} = the ring of integers of Fx. Fx = the residue field of Ox; deg(x) = [Fx : Fq]. For 0 = f ∈ A, deg(f) = the degree of f as a polynomial in T ...
متن کاملArithmetic over Function Fields
These notes accompany lectures presented at the Clay Mathematics Institute 2006 Summer School on Arithmetic Geometry. The lectures summarize some recent progress on existence of rational points of projective varieties defined over a function field over an algebraically closed field.
متن کاملFiniteness properties of arithmetic groups over function fields
We determine when an arithmetic subgroup of a reductive group defined over a global function field is of type FP∞ by comparing its large-scale geometry to the large-scale geometry of lattices in real semisimple Lie groups.
متن کاملFiniteness properties of soluble arithmetic groups over global function fields
Let G be a Chevalley group scheme and B ≤ G a Borel subgroup scheme, both defined over Z. Let K be a global function field, S be a finite non-empty set of places over K , and OS be the corresponding S–arithmetic ring. Then, the S– arithmetic group B(OS) is of type F |S|−1 but not of type FP |S| . Moreover one can derive lower and upper bounds for the geometric invariants Σ(B(OS)). These are sha...
متن کاملComputation of Galois groups over function fields
Symmetric function theory provides a basis for computing Galois groups which is largely independent of the coefficient ring. An exact algorithm has been implemented over Q(t1, t2, . . . , tm) in Maple for degree up to 8. A table of polynomials realizing each transitive permutation group of degree 8 as a Galois group over the rationals is included.
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: International Journal of Number Theory
سال: 2011
ISSN: 1793-0421,1793-7310
DOI: 10.1142/s1793042111004265