1998 Fiscal Year Final Research Report Summary
Finite coverings of algebraic varieties and group schemes over a ring of mixed characteristics
| Project/Area Number |
09640066
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | CHUO UNIVERSITY (1998)
Tokyo Denki University (1997) |
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Principal Investigator |
SUWA Noriyuki Chuo Univ., Fac.of Sci.and Eng., Prof., 理工学部, 教授 (10196925)
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| Project Period (FY) |
1997 – 1998
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| Keywords | Kummer theory / Witt vector / Artin-Hasse exponential / Artin-Schreier Witt theory / algebraic group / formal group / Artin-Tate formula |
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| 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.
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