Algebra Seminar: On rational points, zero cycles and norm principles

Monday, October 14 at 3:30pm to 4:30pm

This is a past event.

Kaprielian Hall (KAP), 245
3620 South Vermont Avenue, Los Angeles, CA 90089

Nivedita Bhaskar, USC

Abstract: A zero cycle on a k-variety X is any element of the free abelian group of closed points of X and its degree is the sum of its coefficients, weighted by the degrees of the residue fields. Any k-rational point of X is a zero cycle of degree one. In this talk, we discuss Serre’s injectivity question which asks whether the converse is true for torsors X under connected linear algebraic groups, i.e. whether such an X admitting a zero cycle of degree one in fact has a rational point. This naturally brings into the picture the so-called norm principles, which examine the behaviour of the images of group morphisms over field extensions from a linear algebraic group into a commutative one with respect to the norm map.

Event Type

Lecture / Talk / Workshop

Campus

University Park Campus

Department
Mathematics
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