University of Cambridge > Talks.cam > Number Theory Seminar > Arithmetic of rational points and zero-cycles on Kummer varieties

Arithmetic of rational points and zero-cycles on Kummer varieties

Add to your list(s) Download to your calendar using vCal

  • UserRachel Newton (University of Reading)
  • ClockTuesday 01 May 2018, 14:30-15:30
  • HouseMR13.

If you have a question about this talk, please contact Jack Thorne.

In 1970, Manin observed that the Brauer group Br(X) of a variety X over a number field K can obstruct the Hasse principle on X. In other words, the lack of a K-point on X despite the existence of points over every completion of K is sometimes explained by non-trivial elements in Br(X). This so-called Brauer-Manin obstruction may not always suffice to explain the failure of the Hasse principle but it is known to be sufficient for some classes of varieties (e.g. torsors under connected algebraic groups) and conjectured to be sufficient for rationally connected varieties and K3 surfaces. A zero-cycle on X is a formal sum of closed points of X. A rational point of X over K is a zero-cycle of degree 1. It is sometimes easier to study the zero-cycles of degree 1 on X, rather than the rational points. Yongqi Liang has shown that for rationally connected varieties, sufficiency of the Brauer-Manin obstruction to the existence of rational points over all finite extensions of K implies sufficiency of the Brauer-Manin obstruction to the existence of zero-cycles of degree 1 over K. I will discuss joint work with Francesca Balestrieri where we extend Liang’s result to Kummer varieties.

This talk is part of the Number Theory Seminar series.

Tell a friend about this talk:

This talk is included in these lists:

Note that ex-directory lists are not shown.

 

© 2006-2019 Talks.cam, University of Cambridge. Contact Us | Help and Documentation | Privacy and Publicity