24 January, 2012 in category english, mathematics by Konrad Voelkel.
Is it possible to prove the Quillen-Suslin theorem analogous to the classical theorem on vector bundles over contractible spaces via representing the vectorbundle-up-to-iso-functor in the homotopy category by infinite Grassmannians?
Tags: affine, A¹, geometry, homotopy, morel, motivic
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14 November, 2011 in category english, mathematics by Konrad Voelkel.
A mind-map overview of the most important single variable complex analysis theorems and some implications between them (complex calculus, first course).
Tags: cheat sheet, complex analysis, diagram, holomorph, learning
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6 November, 2011 in category english, mathematics by Konrad Voelkel.
A closed immersion is finite. A finite morphism is proper, affine and of finite type. Finite morphisms are separated. Open immersions are etale, therefore smooth, thus flat; open immersions are separated. Quasi-compact and locally of finite type implies of finite type. Projective and quasi-finite is the same as finite. Proper morphisms are universally closed. Flat morphisms of finite type are universally open.
Tags: algebraic geometry, cheat sheet, diagram, hartshorne, learning, morphisms, overview, properties, schemes
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13 August, 2011 in category english, life, mathematics by Konrad Voelkel.
Definition of essential manifolds, lens spaces as example of non-aspherical essential manifolds.
Tags: essential, homotopy, manifold
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