BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Francesco Battistoni (Università degli Studi di Milano)
DTSTART:20220324T104500Z
DTEND:20220324T114500Z
DTSTAMP:20260423T053017Z
UID:NTUniPD/4
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NTUniPD/4/">
 Arithmetic equivalence for number fields and global function fields.</a>\n
 by Francesco Battistoni (Università degli Studi di Milano) as part of Num
 ber Theory Seminars at Università degli Studi di Padova\n\n\nAbstract\nTw
 o number fields $K$ and $L$ are said to be arithmetically equivalent if\, 
 for almost every prime number $p$\, the factorizations of $p$ in the rings
  of integers of $K$ and $L$ are analogous (in a precise sense that will be
  explained). A completely similar definition can be given for finite exten
 sions of a function field $F(T)$\, where $F$ is a finite field.\nIn this t
 alk we discuss the concept of arithmetic equivalence in both contexts\, fo
 cusing on the similarities and the differences between the two cases. In p
 articular\, we will show a group-theoretic analogue of the problem and we 
 will explain the relation between arithmetic equivalence and equality of c
 ertain zeta functions (the classical Dedekind zeta function for number fie
 lds\, a more complicated function for function fields). Finally\, we will 
 show how to produce examples of equivalent but not isomorphic fields in bo
 th contexts.\n
LOCATION:https://researchseminars.org/talk/NTUniPD/4/
END:VEVENT
END:VCALENDAR