Finite generation of K-groups of a curve over a finite field: After daniel quillen

DR Grayson - Algebraic K-Theory: Proceedings of a Conference Held …, 2006 - Springer
Algebraic K-Theory: Proceedings of a Conference Held at Oberwolfach, June 1980 …, 2006Springer
The main result in this paper was proved by Quillen by 1974. I have used three sources in
assembling this exposition: notes taken by Hyman Bass at a talk of Quillen's in Oberwolfach
on June 25, 1974; notes from a course given by Quillen at MIT in Spring, 1975; and recent
telephone conversations with Quillen. For a ring of integers in a number field, Quillen had
already shown the groups KiA are finitely generated by September, 1972, when he spoke at
the Battelle conference [Q2]. An examination of the proof there reveals that the only portion …
The main result in this paper was proved by Quillen by 1974. I have used three sources in assembling this exposition: notes taken by Hyman Bass at a talk of Quillen's in Oberwolfach on June 25, 1974; notes from a course given by Quillen at MIT in Spring, 1975; and recent telephone conversations with Quillen.
For a ring of integers in a number field, Quillen had already shown the groups KiA are finitely generated by September, 1972, when he spoke at the Battelle conference [Q2]. An examination of the proof there reveals that the only portion which is not true for every Dedekind domain A with fraction field F is the following pair of assertions.
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