BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Ratko Darda (Sabanci University) DTSTART:20250212T140000Z DTEND:20250212T150000Z DTSTAMP:20260422T103552Z UID:FGC-IPM/54 DESCRIPTION:Title: Malle conjecture for finite group schemes\nby Ratko Darda (Sabanci Un iversity) as part of FGC-HRI-IPM Number Theory Webinars\n\n\nAbstract\nThe Inverse Galois Problem asks whether every finite group G is the Galois gr oup of a Galois extension of the field of rational numbers Q. The Malle co njecture offers a quantitative perspective: it predicts the number of Galo is extensions of Q (or any other number field)\, with G as the Galois grou p\, of bounded "size" (such as the discriminant). In this talk\, we explo re a generalization of the conjecture to finite étale group schemes. We s how how the generalization helps explain inconsistencies of the Malle conj ecture found by Klüners. Additionally\, we discuss the case of the conjec ture when G is a commutative finite étale group scheme\, which generalize s the classical work of Wright on the number of abelian extensions of boun ded discriminant. The talk is based on a joint work with Takehiko Yasuda.\ n LOCATION:https://researchseminars.org/talk/FGC-IPM/54/ END:VEVENT END:VCALENDAR