演講訊息 TALKS

摘要: 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 H\T 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.