Euler systems on Drinfeld modular curves and zeta values


Doç. Dr. SATOSHI KONDO

Tez Türü: Bütünleşik Doktora

Tezin Yürütüldüğü Kurum: Tokyo University, Graduate School of Mathematical Sciences, Department of Mathematical Sciences, Japonya

Tez Danışmanı: Kazuya Kato

Tezin Onay Tarihi: 2022

Tezin Dili: İngilizce

Özet:

(From the introduction)
A conjecture of Beilinson relates elements in the K-group of schemes to special values of L-functions. Beilinson gave such elements in the K-group of modular curves and showed that they were related to the special values of L-functions attached to modular forms ([1],[13]). We follow the analogy between Drinfeld modules of rank two and elliptic curves, and show that the elements in K-theory constructed in [12] are related to, under a regulator map, special values of L-functions attached to automorphic forms in positive characteristic.