BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Andrew V. Sutherland (Massachusetts Institute of Technology) DTSTART:20210628T180000Z DTEND:20210628T185000Z DTSTAMP:20260419T121154Z UID:AFDRT/4 DESCRIPTION:Title: St ronger arithmetic equivalence\nby Andrew V. Sutherland (Massachusetts Institute of Technology) as part of Around Frobenius distributions and rel ated topics II\n\n\nAbstract\nNumber fields K1 and K2 with the same Dedeki nd zeta function\nare said to be arithmetically equivalent. Such number f ields\nnecessarily have the same degree\, signature\, unit group\, discrim inant\,\nand Galois closure\, and the distributions of their Frobenius ele ments\nare compatible in a strong sense: for every unramified prime p the base\nchange of the Q-algebras K1 and K2 to Qp are isomorphic. This need not\nhold at ramified primes\, so the adele rings of K1 and K2 need not be \nisomorphic\, and global invariants such as the regulator and class numbe r\nmay differ.\n\nMotivated by a recent result of Prasad\, I will discuss three stronger\nnotions of arithmetic equivalence that force isomorphisms of some or all\nof these invariants without forcing an isomorphism of numb er fields\, and\npresent examples that address questions of Scott and of G uralnick and\nWeiss\, and shed some light on a question of Prasad. These r esults also\nhave applications to the construction of curves with the same L-function\n(due to Prasad)\, isospectral Riemannian manifolds (due to Su nada)\, and\nisospectral graphs (due to Halbeisen and Hungerbuhler).\n\nPr eprint: https://arxiv.org/abs/2104.01956\n LOCATION:https://researchseminars.org/talk/AFDRT/4/ END:VEVENT END:VCALENDAR