Sponsored by
 
Events
News
 
[ Events ]
 
 

Activity Search
Sort out
Field
 
Year
Seminars  
 
NCTS Seminar on Number Theory
 
13:30 - 14:30, July 4, 2018 (Wednesday)
Lecture Room B, 4th Floor, The 3rd General Building, NTHU
(清華大學綜合三館 4樓B演講室)
Endomorphism Rings of Reductions of Drinfeld Modules
Mihran Papikian (Pennsylvania State University)

Abstract:

Let be the polynomial ring over , and be the field of fractions of . Let be a Drinfeld -module of rank over . For all but finitely many primes , one can reduce modulo to obtain a Drinfeld -module of rank over . The endomorphism ring is an order in an imaginary field extension of of degree . Let be the integral closure of in , and let be the Frobenius endomorphism of
Then we have the inclusion of orders in . We prove that if , then for arbitrary non-zero ideals of there are infinitely many
such that divides the index and divides the index .  
We show that the index is related to a reciprocity law for the extensions of arising from the division points of . In the rank case we describe an algorithm for computing the orders , and give some computational data. (This is a joint work with Sumita Garai.)


 

back to list  
 (C) 2018 National Center for Theoretical Sciences