remove ....

??? "spectrum" .... "cayley-hamilton" .... ??? ..... "zeros of characteristic polynomial" .... ??? infinite-dimensional case ... purely algebraic .... determinant ..... ????? ...... bootstrap ..... ???? ...... tempting false proof of .... ?? cayley-hamilton ?? .... ?? "spectral theorem" ??? ..... ???? ..... ???? ....

pair of commuting operators ....

triple of commuting operators, and grading .... ??? .... hmmmm .... category .... diagram .... "non-commutative geometry" .... ???? ...... category ring ... heisenberg / connes .... ?? "non-commutative" in sense of ... ?? context where "commute" doesn't even parse ... ??? .... ??? algebraic projective geometry / "global algebraic geometry" as maybe aspect of "non-commutative geometry" ??? .... ???? .....

?? anyway, trying to link "removal of point from spectrum of commutative ring" with some definition of "spectrum of operator" involving ... ????? non-invertibility of determinant .... ????? ....

?? characteristic polynomial of operator f as ... ???? polynomial in variable t .... ???? determinant of f - t*[identity operator] ??? ... ??? but how to generalize to arbitrary-dim case ???? ...... ?????? consider kernel and/or cokernel of f - t*[identity operator] ???????? ........ ???????? ..... ???? ....

???? resultant ...... ????? ..... hmmmmm ..... ???? .....

?? coherent sheaf as living over localization iff certain fiber (?? ...) is "trivial" ??? .... .... ????? .....

?? mutual kernel of commuting operators .... ???? co-mutual cokernel ?????? ..... ????....

kernel of homomorphism vs of operator .... confusion ... ??? .... ideal vs fiber .... ?????? ...... ????? ....... ?? hmm, relationship to mystical stuff about "ideal" and "divisor" .... ????? ..... underlying module of (?? good ... "divisorish" ... ??) ideal as "twisted over corresponding codimension 1 subvariety" .... ???? ..... ??? ..... ??? more general codimension ???? ...... ???? .....

?? "kernel and / or cokernel" here as reminding me of "thick subcategory" .... ???? and i was also going to say "quasicoherent artin-wraith glueing", but .... ????? ....

?? "fringe functor" given by some sort of "projective cover" ??? .... ????? .... ??? .... ?? benson ... ??? ....

???? ... ??? also ... ?? "index theorem" ... ???? ....