Seminar on Arithmetic Algebraic Geometry: Real regulator of K_1 of elliptic surfaces
 Date

20121115 10:00 
20121115 12:00
 Place
 Faculty of Science Building #3 Room 413

Speaker/Organizer
 Masanori Asakura

 By the theory of higher Chern class, there is the canonical map from higher Ktheory to the
DeligneBeilinson cohomolgy with coefficients in real numbers, which we call the real
regulator map. As is wellknown, it can be described by extensions of mixed Hodge
structures. Beilinson conjectured the mysterious relationship between the real regulator
and special values of Lfunctions. However, in spite of much efforts by many people,
it is still a widely open problem, together with the fact that the explicit computations of
regulator are very hard in many (most?) cases. In this talk I explain a certain method for
computation of real regulator of K_1 of elliptic surface, where the key ingredient is the
PicardFuchs operator. I have worked out it only to a certain example though it seems to
work as well in more general situation. Required preliminary knowledge is only standard
knowledge of mixed Hodge theory.