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Dec. 2001 Vanishing of certain cohomology sets for $SL_n(R_{\mathcal {M}})$
Nicholas Hine Gajcowski
Proc. Japan Acad. Ser. A Math. Sci. 77(10): 157-160 (Dec. 2001). DOI: 10.3792/pjaa.77.157


Let $\mathcal{M}$ be a maximal ideal of a commutative ring $R$ such that $\sharp(R / \mathcal{M}) < \infty$ and $\operatorname{char} R / \mathcal{M} \ne 2$. Denoting the $\mathcal{M}$-adic completion of $R$ by $R_{\mathcal{M}}$, we will show $H^1(g, SL_n(R_{\mathcal{M}}))$ vanishes for $g = \langle s \rangle$ acting on $SL_n(R_{\mathcal{M}})$ via $A^s = (A^{-1})^t$ where $t$ is the transpose operator.


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Nicholas Hine Gajcowski. "Vanishing of certain cohomology sets for $SL_n(R_{\mathcal {M}})$." Proc. Japan Acad. Ser. A Math. Sci. 77 (10) 157 - 160, Dec. 2001.


Published: Dec. 2001
First available in Project Euclid: 23 May 2006

zbMATH: 1003.20040
MathSciNet: MR1873735
Digital Object Identifier: 10.3792/pjaa.77.157

Primary: 11F75

Keywords: cohomology sets , involution , Lie algebras , orthogonal groups , projective limits , Quadratic forms

Rights: Copyright © 2001 The Japan Academy

Vol.77 • No. 10 • Dec. 2001
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