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7 Nov 2016: What happens over. R? 4. (i) Let V be a vector space, let π1,π2,. , ... 14. Let C be an nn matrix over C, and write C = A iB, where A and B are real nn matrices.

26 Oct 2016: 3. Let V be a 4-dimensional vector space over R, and let {ξ1,ξ2,ξ3,ξ4} be the basis of V dual to the basis{x1,x2,x3,x4} for ... en) is dual. S.J.Wadsley@dpmms.cam.ac.uk - 1 - October 2016. 9. Let A and B be n n matrices over a field F.

28 Nov 2016: Let G be a split reductive group over Z, and let T Gbe a split maximal torus, B a Borel subgroup containing T. ... We write W for the rigid space over L which represents the functor.

18 Aug 2016: for some linear forms 1,. ,n. We multiply by Fxj and sum over j. ... ii) Let A be a 2 n matrix and B an n n alternating matrix over a field K.Suppose that rank A = 2, rank B = n 2 and AB = 0.

27 Apr 2016: Shimura curve MQ(U) defined over F as in [Tho16, 4.2, 4.3]. ... Then RTS is aquotient of a power series ring over ATS = ̂vTRv in h1S,T (Ad.

25 Apr 2016: A necessary condition for x tominimize f over Rn is that f(x) = 0, where. ... The inequalityon the second line holds because the minimum is taken over a larger set.

29 Apr 2016: Contents. 1 Background 51.1 Quadratic forms over F2. 51.2 Theta characteristics. ... If G,H,. are connected algebraic groups over k, then we use gothicletters g,h,.

30 Apr 2016: DEFINITION 1.1. We define the unit sphere bundle SM to be the fibre bundle over M given by. ... X.x;v/ D vi@. @xi. ˇ̌.x;v/C0. @. @vi. ˇ̌.x;v/. :. Since d Og is the identity map on the fibres over x, we have.

18 Jun 2016: 1.1 Definitions. Intension-extension (talk over this); graph of a function. We will use lambdanotation. ‘ ’ ... These proofs are all(morally!) structural inductions over the rectype of the language that is beingreasoned about.