Study of excellent rings and its neighborhood

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(1) In [K], I gave a necessarily and sufficient condition for a Noetherian ring to have an arithmetic Cohen-Macaulayfication.I refine its construction by introducing a new notion, called p-standard sequences.(2) In [K], computed the depth of the canonical module. I compute local cohomology modules of the canonical module.(3) In 1978, Faltings prove the annihilator theorem. In 1982, he conjectured that the annihilator theorem holds under weaker assumption. I give an affirmative answer to his conjecture.(4) In 1991, Hukene [H] proved the uniform Artin-Rees theorem and the uniform Briancon-Skoda theorem. He also conjectured that these theorem hold under weaker assumption. I give an affirmative answer to [H, Conjecture 2.13] concerning these theorems.[F1] G.Faltings, Ueber die Annulatoren lokaler Kohomologiegruppen, Arch.Math. (Basel) 30 (1978), 473--476.[F2] G.Faltings, Der Endlichkeitssatz in der lokalen Kohomologie, Math.Ann.255 (1981), 45--56.[H] C.Huneke, Uniform bounds in noetherian rings, Invent.Math. 107 (1992), 203--223.[K] T.Kawasaki, Finiteness of Cousin cohomologies.