COMMENTS ON “CATEGORICAL REPRESENTATION OF LOCALLY NOETHERIAN LOG SCHEMES”

(1.) The theory exposed in §2 contains errors, as follows: · the necessity asserted in Proposition 2.3, is false; · the isomorphism asserted [unfortunately, without an explicit proof!] in Lemma 2.6, (ii), is false. At the level of main results of the present paper, these errors in the theory of §2, do not affect the proof of Theorem A given in §1, but they do affect the proof — al-though not the validity! — of Theorem B. This result Theorem B is given a correct proof in [MnLgSch], §3 [cf. [MnLgSch], Theorem 3.8, (iii)]. Also, the errors referred to above are discussed in more detail in [MnLgSch], Example 0.3; [MnLgSch], Re-mark 1.4.1. At the level of main results of papers of the author subsequent to the present paper, the only place where the errors in the theory of §2 have an affect is in the portion of the proof of the main result of [ArLgSch] [i.e., [ArLgSch], Theorem 5.1] that involves the theory of [ArLgSch], §4. The affected portions of [ArLgSch], §4, are discussed in more detail in the introduction to [MnLgSch], §4. The main result [ArLgSch], Theorem 5.1, of [ArLgSch] is given a correct proof in [MnLgSch]