Periods and transcendental number theory

introduction

http://golem.ph.utexas.edu/category/2008/05/ambiguity_theory.html

This paper – Ambiguity theory, old and new – is rather fun and would be good to understand thoroughly if we hope to get 2-Galois to do anything important. It’s by Yves André of the ENS, and refers to a comment made by Galois that he was working with a théorie de l’ambiguïté. Good to see Albert Lautman receiving a mention.

For those who want something less introductory, on the same day André has deposited Galois theory, motives and transcendental numbers. Lots there about Kontsevich and Zagier’sPeriods, described in their article of that name in Mathematics Unlimited – 2001 and beyond, pages 771-808, unfortunately now no longer available on the Web.

regulator

regulator = R^n 을 격자로 자른 compact 공간의 부피로 정의

Abel-Jacobi map은

-Chern character map

-대수적 정수론의 Dirichlet regulator

-arithmetic geometry의 Beilinson regulator / Borel regulator

-motivic cohomology의 Hodge realization / de Rham realization

-chow group 의 cycle class map (singular homology의 fundamental class를 sub manifold 버전으로 보는 것)

-Poincare dual

등으로도 일반화

related items

K-theory

books

encyclopedia

[1]http://en.wikipedia.org/wiki/Period_(number)
http://en.wikipedia.org/wiki/Dirichlet%27s_unit_theorem
http://ko.wikipedia.org/wiki/
http://en.wikipedia.org/wiki/regulator
http://en.wikipedia.org/wiki/
http://en.wikipedia.org/wiki/
Princeton companion to mathematics(첨부파일로 올릴것)

blogs

구글 블로그 검색 http://blogsearch.google.com/blogsearch?q=
트렌비 블로그 검색 http://www.trenb.com/search.qst?q=

articles

Transcendence of periods: the state of the art.
- M. Waldschmidt., Pure Appl. Math. Q. 2 (2006), 435-463.
Periods
- Zagier-Kontsevich, 2001
- periods.ps
Algebraic Groups, Hodge Theory, and Transcendence
- G. Wüstholz, , pp. 476–483 in Proc. of the ICM Berkeley 1986 (ed.: A.M. Gleason), AMS, 1987.
Algebraicity of some products of values of the gamma function, Appendix to: P. Deligne, Valeurs de fonctions L et périodes d'intégrales, Proceedings of Symposia in Pure Mathematics, Vol. 33 Part 2, 1979, 313-346.
논문정리
http://www.zentralblatt-math.org/zmath/en/
http://pythagoras0.springnote.com/
http://math.berkeley.edu/~reb/papers/index.html