Finite coverings of algebraic varieties and group schemes over a ring of mixed characteristics
| Project/Area Number |
09640066
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Single-year Grants |
|---|
| Section | 一般 |
|---|
| Research Field |
Algebra
|
|---|
| Research Institution | CHUO UNIVERSITY (1998)
Tokyo Denki University (1997) |
|---|
Principal Investigator |
SUWA Noriyuki Chuo Univ., Fac.of Sci.and Eng., Prof., 理工学部, 教授 (10196925)
|
|---|
| Project Period (FY) |
1997 – 1998
|
| Project Status |
Completed (Fiscal Year 1998)
|
| Budget Amount *help |
¥1,000,000 (Direct Cost: ¥1,000,000)
Fiscal Year 1998: ¥500,000 (Direct Cost: ¥500,000)
Fiscal Year 1997: ¥500,000 (Direct Cost: ¥500,000)
|
|---|
| Keywords | Kummer theory / Witt vector / Artin-Hasse exponential / Artin-Schreier Witt theory / algebraic group / formal group / Artin-Tate formula / Artin-Hasse-exponentiol / group scheme / Kummer theory / Artin-Schreier-Witt theory / Witt Vector / Artin-Hasse exponential series |
|---|
| Research Abstract |
(1) Define a formal power series E_p(U, LAMBDA ; T) epsilonQ[U,LAMBDA][[T]] by
E_p(U, LAMBDA ; T)=(1+$KT)^<U/(bda)>II^^*__(1+LAMBDA^<pk>T^<pk>)^<pk/{((LAMBDA)/)^<pk>-((LAMBDAk)/)pk-1>}
The Artin-Hasse exponential seiries E_p(T) was defined by
E<@D2p@>D2(T)=exp(SIGMA<@D6*(/)k=0@>D6<@D7T<@D1pk@>D1(/)p<@D1k@>D1@>D7) (Artin-Hasse exponential series).
We have proved the equality
<<numerical formula>>
E_p(T) corresponds to exp t and E_p (U, LAMBDA ; T) to (1+lambdat)^<1/lambda> in the well known formula
<lambda * 0>___(1+lambdat)^<1/lambda> = expt
(2) We have improved some results by Gouvea and Yui on special values of the congruence zeta function and the discriminant on the intersection forms of algebraic cycles for a diagonal hypersurfaces, correcting defects of their method.
|
Report
(3 results)
Research Products
(15 results)
