We consider fields K with an abstract notion of dimension as stated by Pillay and Poizat in their paper of 1995. We prove that, for every finite extension L of K and for every finite Galois extension L-1 of L, the Brauer group Br(L-1/L) is finite. Moreover, given an algebraic group G defined over L, we have that H-1 (L1/L, G) is finite. (c) 2006 Elsevier Inc. All rights reserved.
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