摘要:
Let K be a function field over the fnite field Fq. Let A be the ring of elements
Let K be a function field over the fnite field Fq. Let A be the ring of elements
of K that are integral outside a fixed place of K. The simplest,, but already highly
nontrivial example is A being the polynomial ring Fq[t] and K the rational function
field Fq(t).
The Drinfeld modular group GL2(A) and its action on its Bruhat-Tits tree T play
a similarly important role in function field arithmetic as the action of the modular
group SL2(Z) on the complex upper halfplane plays in classical number theory.
For finite index subgroups H of GL2(A) the quotient HT is essentially a finite
graph. It encodes information about the group-theoretic structure of H, about
the Drinfeld modular curve associated to H, and about the classification of elliptic
curves over K.