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SUMMARY:Giancarlo Lucchini Arteche (Universidad de Chile)
DTSTART:20201216T170000Z
DTEND:20201216T180000Z
DTSTAMP:20260416T043507Z
UID:NTRV/6
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NTRV/6/">Loc
 al-global principles for homogeneous spaces over some geometric global fie
 lds</a>\nby Giancarlo Lucchini Arteche (Universidad de Chile) as part of N
 umber Theory and Representations in Valparaiso\n\n\nAbstract\nLocal-global
  principles are a classical type of problem in Number Theory\, both over n
 umber fields and over global fields in positive characteristic. Concerning
  the local-global principle for the existence of rational points\, there i
 s a classic obstruction known as the Brauer-Manin obstruction\, which is c
 onjectured to explain all failures of this principle for homogeneous space
 s of connected linear groups.\nIn the last few years\, there has been an i
 ncreasing interest in fields of a more ``geometric" nature that are amenab
 le to local-global principles as well. These include\, for instance\, func
 tion fields of curves over discretely valued fields\, by analogy with the 
 positive characteristic case. It is in this context that I will present re
 cent work with Diego Izquierdo on local-global principles for homogeneous 
 spaces with connected stabilizers. We will see that\, although some of the
  known results for number fields have direct analogs (that can be obtained
  in the same way)\, the particularities of these new fields bring up new c
 ounterexamples that cannot be explained by the Brauer-Manin obstruction\, 
 contrary to the number field case.\n
LOCATION:https://researchseminars.org/talk/NTRV/6/
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