BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Cristiana Bertolin DTSTART:20230517T140000Z DTEND:20230517T150000Z DTSTAMP:20260422T104855Z UID:FGC-IPM/35 DESCRIPTION:Title: Periods of 1-motives and their polynomials relations\nby Cristiana Be rtolin as part of FGC-HRI-IPM Number Theory Webinars\n\n\nAbstract\nThe in tegration of differential forms furnishes an isomorphism between the De Rh am and the Hodge realizations of a 1-motive M. The coefficients of the mat rix representing this isomorphism are the so-called "periods" of M.\n In t he semi-elliptic case (i.e. the underlying extension of the 1-motive is an extension of an elliptic curve by the multiplicative group)\, we compute explicitly these periods. \n \nIf the 1-motive M is defined over an algebr aically closed field\, Grothendieck's conjecture asserts that the transcen dence degree of the field generated by the periods is equal to the dimensi on of the motivic Galois group of M. If we denote by I the ideal generated by the polynomial relations between the periods\, we have that "the numbe rs of periods of M minus the rank of the ideal I is equal to the dimension of the motivic Galois group of M"\, that is a decrease in the dimension o f the motivic Galois group is equivalent to an increase of the rank of the ideal I. We list the geometrical phenomena which imply the decrease in th e dimension of the motivic Galois group and in each case we compute the po lynomials which generate the corresponding ideal I.\n\nZoom Meeting ID: 85 6 1386 0958 Passcode: 513992\n LOCATION:https://researchseminars.org/talk/FGC-IPM/35/ END:VEVENT END:VCALENDAR