Daniel Krashen

Abstract:   In this talk we investigate issues that relate to zero cycles on varieties which are twisted forms of Grassmanninans or Quadric hypersurfaces. On example would be the (projective completion of) the zeros of the polynomial

x² + y² + 1

considered ove the real numbers. Note that this has many complex points, but no real solutions. Given such a variety X, one may consider the degree map which takes a zero cycle (a formal linear combination of points on X) to an integer (the sum of the coefficients, or, 'number of points'). The focus of the talk is to determine what, if any, information is lost by this map.

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