A nondegeneracy result for a nonlinear elliptic equation by Grossi M. PDF

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These include all of the results about 7L-orders mentioned above, as well as some properties of applied to 2p orders. Then, for example, show, p-adically closed in in Section 2b, p-adic logarithms are that for any (i. , GL(21) that 7l-order K1(21) 21, E(21) is is Hausdorff in the p-adic topology). Applications of the reduced norm 2a. K: A* - F* norm homomorphtsm be any extension which splits Then for any a E A*, E®FA -4-> Mn(E). 1(iv) above). of A for Cal(E/F) Mn(E) Furthermore, E/F if splitting field E.

Modules have finite projective resolutions. Ki(M(IR)) = Ki(7R) JR-module M, and Ki(M(I[1])) = Ki(IR[l]). M = ®(p), and each M(p) It For any has a filtration by So by devissage (Quillen [1, Theorem 4]), R /Jp modules. Jp). (Mt(T)) = ® Ki(i P In case semisimple, K1(]IVJ) p4'ISKI(m)I. ld. (i), SKl(At) = - Im[K1(Th/J) has order prime to p Kl(1)]. 16(iii), and so o Bimodule-induced homomorphisms and Morita equivalence Define the category of "rings with bimodule morphisms" to be the category whose objects are rings; and where and S, isomorphism classes of (S,R)-bimodules SMR generated and projective as a left S-module.

Let Furthermore, is a p-group if pj'IK1(R)I Proof if R R R be a finite ring. 14(i), are both finite. R = ni_1Mri(Di), and hence fields. R and K2(R) Then K1(R) p); R* surjects onto If R H2(E5(R)) K1(R). onto are (it) K2(R) and (iii) is semisimple and has p-power order for some prime Theorem 1], there is a surjection of and it is often necessary to for ideals I C 21 of finite 21, p. By Dennis [1, K2(R). So K1(R) is semisimple, then by the Wedderburn where the D. Then GL(R) = [[k=1CL(Di), are finite division algebras E(R) = ((i=1E(D1); and hence 36 BASIC ALGEBRAIC BACKGROUND CHAPTER 1.

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A nondegeneracy result for a nonlinear elliptic equation by Grossi M.

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