Fields of definition of elliptic fibrations on covers of certain extremal rational elliptic surfaces
Freitag, 12.6.20, 10:30-11:30, virtueller Raum 404
K3 surfaces have been extensively studied over the past decades for\nseveral reasons. For once, they have a rich and yet tractable geometry\nand they are the playground for several open arithmetic questions.\nMoreover, they form the only class which might admit more than one\nelliptic fibration with section. A natural question is to ask if one\ncan classify such fibrations, and indeed that has been done by several\nauthors, among them Nishiyama, Garbagnati and Salgado.\nIn this joint work with A. Garbagnati, C. Salgado, A. Trbović and R.\nWinter we study K3 surfaces defined over a number field k which are\ndouble covers of extremal rational elliptic surfaces. We provide a list\nof all elliptic fibrations on certain K3 surfaces together with the\ndegree of the field extension over which each genus one fibration is\ndefined and admits a section. We show that the latter depends, in\ngeneral, on the action of the cover involution on the fibers of the\ngenus one fibration.
"(Ir)rationality of L-values"
Freitag, 26.6.20, 10:30-11:30, virtueller Raum 404
Euler’s beautiful formula\nζ(2n) = −\n(2πi) 2n\nB 2n .\n2(2n)!\ncan be seen as the starting point of the investigation of special values of L-\nfunctions. In particular, Euler’s result shows that all critical zeta values are ra-\ntional up to multiplication with a particular period, here the period is a power of\n(2πi). Conjecturally this is expected to hold for all critical L-values of motives.\nIn this talk, we will focus on L-functions of number fields. In the first part of the\ntalk, we will discuss the ’critical’ and ’non-critical’ L-values exemplary for the\nRiemann zeta function. Afterwards, we will head on to more general number\nfields and explain our recent joint result with Guido Kings on the algebraicity\nof critical Hecke L-values for totally imaginary fields up to explicit periods.
"(Ir)rationality of L-values"
Freitag, 26.6.20, 10:30-11:30, v404
Euler’s beautiful formula\nζ(2n) = −\n(2πi) 2n\nB 2n .\n2(2n)!\ncan be seen as the starting point of the investigation of special values of L-\nfunctions. In particular, Euler’s result shows that all critical zeta values are ra-\ntional up to multiplication with a particular period, here the period is a power of\n(2πi). Conjecturally this is expected to hold for all critical L-values of motives.\nIn this talk, we will focus on L-functions of number fields. In the first part of the\ntalk, we will discuss the ’critical’ and ’non-critical’ L-values exemplary for the\nRiemann zeta function. Afterwards, we will head on to more general number\nfields and explain our recent joint result with Guido Kings on the algebraicity\nof critical Hecke L-values for totally imaginary fields up to explicit periods.