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21 Apr 2013: A) g : X X′ is étale over Y ′(B) Γ(X,OX) = K is a field. ... ar,. where sum ranges over complete set of representatives of congruence classes modulop in Q(ζm).

15 Mar 2013: and pseudo-maps over A and B; andS-PsAlgA and S-PsAlgK, the corresponding 2-categories of pseudo-algebras.The classic reference for material relating to this kind of situation is ... In particularthere is none in the case of Vectk, the category of vector

20 Feb 2013: the product runs over embeddings τ : L Csuch that ι1τ induces the place v of L. ... for any F-algebra R. We may choose an order OB B, stable under †, so that OB,w is maximal for anyplace w of E split over F.

25 Feb 2013: The converse isobtained by going over the same arguments backwards and is left as an exercise. ... Definition. Let f : {|z| > R} C be holomorphic. Then f() = a0 (a0 C) withmultiplicity m if h(z) = f(1/z) extends holomorphically over zero by putting h(0) =

13 Jan 2013: Multiplication is distributive over addition; that is, a(b c) = ab ac for alla,b,c F. ... 3 ) =. {a b. 3 : a,b Q. },. Everything we will discuss works over any field, but it’s best to have R and C in mind,since that’s what