4 INTRODUCTION
R E L A T I O N S H I P C H A R T F O R T I G H T C L O S U R E
A N D IT S A P P L I C A T I O N S
IMPROVED
HOMOLOGICAL
CONJECTURES,
VANISHING THEORE M
FOR MAP S O F T O R
ARITHMETIC
MACAULAYFICATIONS
X
BIG
COHEN-MACAULAY
ALGEBRAS, R+, AN D
SOLID CLOSUR E
X
VANISHING THEOREM S
ON HOMOLOGY :
GRAUERT-
RIEMENSCHNEIDER,
KODAIRA, ETC .
\
PHANTOM
HOMOLOGY
1
/ TIGH T \
I CLOSUR E J
i
DIRECT SUMMAND S
OF REGULA R RING S
AND
INVARIANT THEOR Y
DIFFERENTIAL
OPERATORS AN D
STRONGLY
F-REGULAR RING S
UNIFORM
ARTIN-REES
THEOREMS
BRIANgON-SKODA
THEOREMS, INTEGRA L
CLOSURES, AN D
RATIONAL
SINGULARITIES
\
CLASSIFICATION O F
SINGULARITIES:
F-PURE , F-RATIONAL ,
AND
F-REGULAR RING S
X
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