BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Andoni Zozaya (University of Ljubljana) DTSTART:20240516T143000Z DTEND:20240516T152000Z DTSTAMP:20260416T215641Z UID:GiG2024/4 DESCRIPTION:Title: Linearity of compact analytic groups over domains of characteristic zero\nby Andoni Zozaya (University of Ljubljana) as part of Groups in Galway 2024\n\nLecture held in McMunn lecture theatre.\n\nAbstract\nA $p$-adic a nalytic group is a topological group that is endowed with an analytic mani fold structure over $\\mathbb{Z}_p$\, the ring of $p$-adic integers. This definition can be extended by considering the manifold structure over more general pro-$p$ domains\, such as the power series rings $\\mathbb{Z}_p[[ t_1\, \\dots\, t_m]]$ or $\\mathbb{F}_p[[t_1\, \\dots\, t_m]]$ (where $\\m athbb{F}_p$ denotes the finite field of $p$ elements).\n\nLazard establish ed already in the 1960s that compact $p$-adic analytic groups are linear\, as they can be embedded as a closed subgroup within the group of invertib le matrices over $\\mathbb{Z}_p$. Nonetheless\, the question of the linear ity of analytic groups over more general domains remains unsolved.\n\nIn t his talk\, we shed some light to this question by proving that when the co efficient ring is of characteristic zero\, every compact analytic group is linear. We will provide background on the problem and outline the strateg y of our argument.\n\nJoint with M. Casals-Ruiz.\n LOCATION:https://researchseminars.org/talk/GiG2024/4/ END:VEVENT END:VCALENDAR