most recent 30 from http://mathoverflow.net 2013-06-20T07:03:57Z http://mathoverflow.net/feeds/user/17309 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/79224/universal-categorical-quotient google 2011-10-27T02:32:19Z 2012-10-28T12:26:13Z

<p>I have a foolish question. But I don't understad it. Could you help me?</p> <p>Why the following 2 are equivalent? 1. (Y,f) is a universal categorical quotient of X by G. 2. for all affine schemes Y',and morphisms Y' -> Y, if f':X' -> Y' is the base extension,then (Y',f') is a categorical quotient of X' by G.</p>

http://mathoverflow.net/questions/80669/affine-morphism google 2011-11-11T10:12:47Z 2012-01-06T13:22:12Z

<p>Let G, X and Y are algebraic schemes over k.(k:field) Assume that G is affine, and that the action is proper. Then f:X -> Y is affine. This is the Proposition0.7 in 'GIT(mumford &amp; Fogarty)' I don't understand the part of the proof of this Prop.</p> <p>g: G×Y -> X is a proper morphism. P_2: G×Y -> Y is the second projection and affine morphism. and f·g=p_2. The author says "by Chevalley's Theorem(EGA 2, Theorem 6.7.1), f is affine". I can't draw it. Please, help me...</p> <p>(*Chevalley's Thm: X: affine scheme, Y: noetherian pre-scheme, f: x -> Y is a finite surjective morphism Then Y is also affine.)</p>

http://mathoverflow.net/questions/80264/property-of-dual-isogeny google 2011-11-07T02:32:39Z 2011-11-07T02:32:39Z

<p>Let G:E -> E' and H: E->E' be isogenies between elliptic curves. Then (G+H)^=G^+H^ (G^ means dual isogeny od G).</p> <p>I'm reading "The Arithmetic of Elliptic Curves[Silverman]" Actually it's a part of Theorem in Chap3.6. I can't understand its proof. In particular, "ord_{P_1}(f)=e_{G}(p_1)" this equality. (Sorry,I can't whole content of proof.) Somebody, help me!</p>

http://mathoverflow.net/questions/73489/arithmetic-genus-of-nonsingular-curve-of-degree-d-in-pp3 google 2011-08-23T12:40:07Z 2011-08-23T13:12:55Z

<p>The arithmetic genus of nonsingular curve C of degree d in PP^3 over an algebraically closed field is less than or equal to 1/2(d-1)(d-2). I must show it by comparing C with a suitable projection from a point into PP^2. How can I prove it?</p>

http://mathoverflow.net/questions/73401/give-an-example-about-flatness google 2011-08-22T12:35:19Z 2011-08-22T15:15:54Z

<p>Please give an example of a flat family {X_t} of closed subschemes of PP^n such that the family of projective cones of X_t is not a flat family in PP^{n+1}.</p> <p>I still could not find...</p>