CONTROL THEOREMS OF COHERENT SHEAVES ON SHIMURA VARIETIES OF PEL TYPE

被引:41
作者
Hida, Haruzo [1 ]
机构
[1] Univ Calif Los Angeles, Dept Math, Los Angeles, CA 90095 USA
关键词
Hecke algebra; Hecke operator; p-adic automorphic forms; p-adic family;
D O I
10.1017/S1474748002000014
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
An exact control theorem is proven for nearly ordinary p-adic automorphic forms on symplectic and unitary groups over totally real fields if the algebraic group is split at p. In particular, a given nearly ordinary holomorphic Hecke eigenform can be lifted to a family of holomorphic Hecke eigenforms indexed by weights of the standard maximal split torus of the group. Their q-expansion coefficients are Iwasawa functions on the Iwasawa algebra of Z(p)-points of the split torus. The method is applicable to any reductive algebraic groups yielding Shimura varieties of PEL type under mild assumptions on the existence of integral toroidal compactification of the variety. Even in the Hilbert modular case, the result contains something new: freeness of the universal nearly ordinary Hecke algebra over the Iwasawa algebra, which eluded my scrutiny when I studied general theory of the p-adic Hecke algebra in the 1980s.
引用
收藏
页码:1 / 76
页数:76
相关论文
共 55 条
[1]  
[Anonymous], 1997, CBMS REGIONAL C SERI
[2]  
[Anonymous], 1974, TIFR STUDIES MATH
[3]  
[Anonymous], 1965, Geometric Invariant Theory
[4]  
BLASIUS D., 1989, MSRI PUBLICATION, V16, P32
[5]  
CHAI CL, 1985, LMS LECT NOTE SERIES, V107
[6]  
Deligne P., 1969, PUBL MATH-PARIS, V36, P75
[7]  
Deligne P., 1979, P S PURE MATH 2, V2, P247
[8]  
Dieudonne J., 1965, ELEMENTS GEOMETRIE A, V24, P5
[9]  
Faltings G., 1990, ERGEBNISSE MATH IHRE
[10]  
FUJIWARA K, 1989, THESIS U TOKYO