[PDF][PDF] A cohomological interpretation of Brauer groups of rings.
RT Hoobler - 1980 - projecteuclid.org
1980•projecteuclid.org
Quillen's proof of the Serre conjecture introduced a new tool for passing from local to global
results on affine schemes. We use this to prove the theorem below characterizing the image
of the injection i: Br {X)—• H2 (Xct, Gm) when X= Spec A, is a regular scheme. A result of M.
Artin then allows us to conclude that Br (X)= H% Xet, Gm) if X= Spec A is a smooth, affine
scheme over a field. For such rings, this proves the Auslander Goldman conjecture [2], Br {Λ)—
f) Br (Ap), peP (A), the set of height one primes of A. We begin with following theorem.
results on affine schemes. We use this to prove the theorem below characterizing the image
of the injection i: Br {X)—• H2 (Xct, Gm) when X= Spec A, is a regular scheme. A result of M.
Artin then allows us to conclude that Br (X)= H% Xet, Gm) if X= Spec A is a smooth, affine
scheme over a field. For such rings, this proves the Auslander Goldman conjecture [2], Br {Λ)—
f) Br (Ap), peP (A), the set of height one primes of A. We begin with following theorem.
Quillen's proof of the Serre conjecture introduced a new tool for passing from local to global results on affine schemes. We use this to prove the theorem below characterizing the image of the injection i: Br {X)—• H2 (Xct, Gm) when X= Spec A, is a regular scheme. A result of M. Artin then allows us to conclude that Br (X)= H% Xet, Gm) if X= Spec A is a smooth, affine scheme over a field. For such rings, this proves the Auslander Goldman conjecture [2], Br {Λ)—f) Br (Ap), peP (A), the set of height one primes of A. We begin with following theorem.
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