Download e-book for kindle: Drinfeld Modular Curves by Ernst-Ulrich Gekeler

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  • February 13, 2018
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By Ernst-Ulrich Gekeler

ISBN-10: 3540172017

ISBN-13: 9783540172017

ISBN-10: 3540473866

ISBN-13: 9783540473862

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Example text

Is a b e l i a n (A/n)* in let n ~ A a subgroup ramification . The of Decomposing properties field n into primary (see(l,3)) , it is to show: Theorem. H(D(¢,n)) is the field H(n) , independently of ¢ . ~... > O a l ( H ( n ) a I acts on D(%,n) by 1-1attice CA is s g n - n o r m a l i z e d . 13 A Corollary. lattices. 1), 3. In on Some are x with Let a c A section a N we ~(A) of A by the condition by elements special. determined shall of up to m u l t i p l i c a t i o n choose a specific be value of Uw for lemmata needed for the computation a l-unit an and i 6 Z ideal and -linear q a/fa .

Namely, are 45 {classes of ends of T } = Pic M F = F~ 6 G(K) and to describe with ~(~) : s a F-invariant function -I F~ , and we will at ~ . The group of of . Like A the lations ~' hood of of z I ~ such zero 0 > z+b in ~ b C e~ I . e. f = f o m is i n v a r i a n t v of f at s by that of contains fractional is i n v a r i a n t is a n identifies instance, to adjoin (Fs)~-1 with . There = 6 . P(1) So l e t s 6 ~I(K) function f on function function 6 • h .

E. i = c 1 - q i. (a,A) li(a,cA) 1 For lattices A c A' corresponding in morphism C of the of D r i n f e l d same rank, modules let (compare u(A,A') be (I 2 . 3 - 2 . 5 ) ) . 4) On the = ~ o eA several we a other have and "canonical" for : 1 -I for (u) = I normalizations of the polynomial a 6 A • ~(A,a-IA) hand, D(~) • A = Ca an ideal n c A and u = u(A,n-IA) , ~ ; for 18 is %i ~ n the uniquely determined morphism i of H a y e s [36] w h i c h s a t i s f i e s lattice * A i(~) n * % into : I . 6) the Namely, the If all we have ~ of A side the scalar of GL(r,Af) * ~ i is matrix in the associated defined in (I 3 .

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Drinfeld Modular Curves by Ernst-Ulrich Gekeler


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