연사 : Masanori Asakura 교수 (Hokkaido 대학교)
초청자 : 박진현 (자연 4402, T. 2734)
일시 : 2009/1/12 13:30~15:00 (자연과학동 1409)
제목 : p-adic regulator on indecomposable K_1 of elliptic surface (part I)
This is a joint work with K. Sato. By the theory of higher Chern classes, there are regulator maps from algebraic K-groups to generalized cohomology groups. In this talk we discuss K_1 and the regulator map to p-adic etale cohomology group. There are a lot of open problems about it, in particular, the Bloch-Kato conjecture predicts the bijectivity onto certain subspace of Galois cohomology.
In general K_1 is decomposed into the decomposable part and indecomposable part. The former is more or less trivial. However the latter is usually difficult to understand and even constructing a nontrivial class often plays a central role in the study of K_1.
In this talk we give a general method of constructing indecomposable elements in K_1 of elliptic surfaces whose p-adic regulators do not vanish. It allows us to construct a non-trivial image in the finite part of Galois cohomology.
The crucial technique is the theory of syntomic cohomology by Fontaine and Messing. I will explain how the syntomic cohomology works in our method and I will give explicit examples of indecomposable elements.