Tate Uniformization of Drinfeld Modules and Compactifications of Drinfeld Modular Varieties
ثبت نشده
چکیده
Let us fix the usual notation • C is a geometrically connected smooth projective curve over a finite field Fq. • ∞ ∈ C is a closed point. • F = Fq(C) is the function field of C. • A = H(C − {∞},OC) is the ring of functions on C that are regular outside ∞. • Â = lim0 6=I⊂AA/I and Af = Â⊗A F . • F∞ is the completion of F at ∞ with valuation ring O∞. The ring A is discrete inside F∞, and the absolute value of F∞ is normalized via |a|∞ = #|A/a| for any 0 6= a ∈ A. • C∞ is the completed algebraic closure of F∞. • For a ring R of characteristic p, R{τ} ' EndG(Ga,R) is the Frobenius twisted polynomial arising. The main objects under consideration are:
منابع مشابه
Uniformizing the Stacks of Abelian Sheaves
Elliptic sheaves (which are related to Drinfeld modules) were introduced by Drinfeld and further studied by Laumon–Rapoport–Stuhler and others. They can be viewed as function field analogues of elliptic curves and hence are objects “of dimension 1”. Their higher dimensional generalizations are called abelian sheaves. In the analogy between function fields and number fields, abelian sheaves are ...
متن کاملTwists of Drinfeld–Stuhler Modular Varieties
Let A be a maximal (or more generally a hereditary) order in a central simple algebra over a global field F of positive characteristic. We show that certain modular scheme of A-elliptic sheaves– for different A – are twists of each other and deduce that the uniformization at ∞ and the Cherednik-Drinfeld uniformization for these varieties are equivalent. 2010 Mathematics Subject Classification: ...
متن کامل2 2 N ov 2 00 4 DRINFELD MODULAR CURVE AND WEIL PAIRING
In this paper we describe the compactification of the Drin-feld modular curve. This compactification is analogous to the compact-ification of the classical modular curve given by Katz and Mazur. We show how the Weil pairing on Drinfeld modules that we defined in earlier work gives rise to a map on the Drinfeld modular curve. We introduce the Tate-Drinfeld module and show how this describes the ...
متن کاملIntroduction to Drinfeld Modules
(1) Explicit class field theory for global function fields (just as torsion of Gm gives abelian extensions of Q, and torsion of CM elliptic curves gives abelian extension of imaginary quadratic fields). Here global function field means Fp(T ) or a finite extension. (2) Langlands conjectures for GLn over function fields (Drinfeld modular varieties play the role of Shimura varieties). (3) Modular...
متن کاملThe Sato-tate Law for Drinfeld Modules
We prove an analogue of the Sato-Tate conjecture for Drinfeld modules. Using ideas of Drinfeld, J.-K. Yu showed that Drinfeld modules satisfy some Sato-Tate law, but did not describe the actual law. More precisely, for a Drinfeld module φ defined over a field L, he constructs a continuous representation ρ∞ : WL → D× of the Weil group of L into a certain division algebra, which encodes the Sato-...
متن کامل