Finitely Generated Projective Module over the Tate Algebra
Date Issued
2012
Date
2012
Author(s)
Chiu, Ching-Heng
Abstract
"Serre''s Conjecture", referred to the famous statement made by J.-P. Serre in 1955, to the e ect that one did not know if nitely generated modules were free over a polynomial ring k[t1; : : : ; td], where k is a eld. Serre made some
progress towards a solution in 1957 when he proved that every nitely generated projective module over a polynomial ring over a eld was stably free. The problem remained open until 1976, when Daniel Quillen and Andrei Suslin independently proved that the answer was a rmative. Kiran S. Kedlaya have proved the case in Tn, the Tate algebra. Lindel-Lutkebohmert and Mohan Kumar did the case of k[[X]][T], polynomial ring over formal power series ring. In this paper, we try to use the similar method to solve the case that the polynomial ring is replaced by Tn[T], polynomial ring over Tate algebra.
Subjects
Finitely Generated Projective Module
Type
thesis
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