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18 Feb 2010: abelian category of “mixed motives”. The ultimate definition of such a category remains to be found. ... φ : IK T. Here T/K is a number field and there exist integers a, b with ab = w such that.

15 Oct 2010: On the other hand, show that if fn does not converge uniformly to f, then we can find aconvergent sequence xm x in [a, b] such that fn(xn) does not ... Give an example of a sequence of uniformly continuousfunctions fn on R, such that fn converges

29 Apr 2010: c) Give a topology on R which is neither trivial nor discrete such that every open set isclosed (and vice-versa). ... Prove the following:. (a) G is homogeneous: given any x, y G there is a homeomorphism φ : G G such thatφ(x) = y.

8 Nov 2010: a linear func-tional θ V such that θ(x) 6= θ(y).(b) Suppose that V is finite dimensional. ... If no such subspaceexists, show that there exists a basis v, α(v),.

17 Dec 2010: such that. MIA A M/B. ll 1r MA oh_ MB. commuts up to natural isomorphism. ... For g : Y-, B in M/B we expect IIh 0 Y E M/A to be such that a fibre (II,, 0 Y)n is the modest set of sections

17 Dec 2010: clopen sets guxantecd by oil’s being separated. For each B c A such that V,, J: fl,. ... such that WAcJ,=fl where A(J) =; l_j {Ai 1 iE.7}. B! ( )

17 Dec 2010: clopen sets guxantecd by oil’s being separated. For each B c A such that V,, J: fl,. ... such that WAcJ,=fl where A(J) =; l_j {Ai 1 iE.7}. B! ( )

25 Nov 2010: 6 and 12, related by c34 c26 = 1728, such that(i) The ring of invariants K[Xn]. ... in K[c4,c6] such that. D(λ,µ) = D(λa µDb,λb µD. a)/D(a,b). c4(λ,µ) = c4(λa µDb ,λb µDa. ).

19 Oct 2010: Many peoplestill study them for practical purposes such as elliptic curve cryptography, but I. ... becomes just Q. Therefore refers to the fact that we replace this componentin the image with b Q, chosen such that NQ[θ].

29 Jan 2010: There exists such a basechange overwhich factors as a product of isogenies of prime degree. ... the smallest closed subset of V k[r] such thatV k[r]V k[r1] is smooth over S.