[Turkmath:6119] FGC-HRI-IPM number theory seminars::[Cristiana Bertolin][May 17, 5pm]

[Özlem Ejder]

Dear all,

Cristiana Bertolin (Università di Padova) is our speaker in the FGC-HRI-IPM
Number Theory Seminar this upcoming week.

*Date and Time:* Wednesday May 17, at 17:00 Istanbul time.

*Title: *Periods of 1-motives and their polynomials relation

*Abstract: *The integration of differential forms furnishes an isomorphism
between the De Rham and the Hodge realizations of a 1-motive M. The
coefficients of the matrix representing this isomorphism are the so-called
"periods" of M.  In the 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.

If the 1-motive M is defined over an algebraically closed field,
Grothendieck's conjecture asserts that the transcendence degree of the
field generated by the periods is equal to the dimension 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 numbers 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 of 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 the
dimension of the motivic Galois group and in each case we compute the
polynomials which generate the corresponding ideal I.

*Zoom Meeting ID: *856 1386 0958
*Passcode: *513992
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