BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Andrea Ferraguti (Università di Torino) DTSTART:20241204T140000Z DTEND:20241204T150000Z DTSTAMP:20260422T104904Z UID:FGC-IPM/51 DESCRIPTION:Title: Frobenius and settled elements in iterated Galois extensions\nby Andr ea Ferraguti (Università di Torino) as part of FGC-HRI-IPM Number Theory Webinars\n\n\nAbstract\nUnderstanding Frobenius elements in iterated Galoi s extensions is a major goal in arithmetic dynamics. In 2012 Boston and Jo nes conjectured that any quadratic polynomial f over a finite field that i s different from x^2 is settled\, namely the weighted proportion of f-stab le factors in the factorization of the n-th iterate of f tends to 1 as n t ends to infinity. This can be rephrased in terms of Frobenius elements: gi ven a quadratic polynomial f over a number field K\, an element \\alpha in K and the extension K_\\infty generated by all the f^n-preimages of \\alp ha\, the Frobenius elements of unramified primes in K_\\infty are settled. In this talk\, we will explain how to construct uncountably many non-conj ugate settled elements that cannot be the Frobenius of any ramified or unr amified prime\, for any quadratic polynomial. The key result is a descript ion of the critical orbit modulo squares for quadratic polynomials over lo cal fields. This is joint work with Carlo Pagano.\n LOCATION:https://researchseminars.org/talk/FGC-IPM/51/ END:VEVENT END:VCALENDAR