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SUMMARY:Hasse principle for intersections of two quadrics via Kummer surfa
 ces - Adam Morgan (Cambridge)
DTSTART:20241105T143000Z
DTEND:20241105T153000Z
UID:TALK220117@talks.cam.ac.uk
CONTACT:Jef Laga
DESCRIPTION:I will discuss recent work with Skorobogatov in which we estab
 lish the Hasse principle for a broad class of degree 4 del Pezzo surfaces 
 (including all those with irreducible characteristic polynomial)\, conditi
 onal on finiteness of relevant Tate--Shafarevich groups. A corollary of th
 is work is that the Hasse principle holds for smooth complete intersection
 s of two quadrics in P^n for n\\geq 5\, conditional on the same conjecture
 .  The proof involves the study of the Hasse principle and Brauer—Manin 
 obstruction on auxiliary Kummer surfaces.
LOCATION:MR13
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