Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Geometric idealizers   Let X be a projective variety, $\sigma$ an automorphism of X, L a
$\sigma$-ample invertible sheaf on X, and Z a closed subscheme of X. Inside the
twisted homogeneous coordinate ring $B = B(X, L, \sigma)$, let I be the right
ideal of sections vanishing at Z. We study the subring R = k + I of B. Under
mild conditions on Z and $\sigma$, R is the idealizer of I in B: the maximal
subring of B in which I is a two-sided ideal.
  We give geometric conditions on Z and $\sigma$ that determine the algebraic
properties of R, and show that if Z and $\sigma$ are sufficiently general, in a
sense we make precise, then R is left and right noetherian, has finite left and
right cohomological dimension, is strongly right noetherian but not strongly
left noetherian, and satisfies right $\chi_d$ (where d = \codim Z) but fails
left $\chi_1$. We also give an example of a right noetherian ring with infinite
right cohomological dimension, partially answering a question of Stafford and
Van den Bergh. This generalizes results of Rogalski in the case that Z is a
point in $\mathbb{P}^d$.

37
The categories of this paper are: supr-con
4
The categories of this paper are: cond-mat
34
The categories of this paper are: chem-ph
9
The categories of this paper are: nlin
17
The categories of this paper are: q-fin
36
The categories of this paper are: cmp-lg
5
The categories of this paper are: gr-qc
16
The categories of this paper are: stat
25
The categories of this paper are: patt-sol
30
The categories of this paper are: q-alg
23
The categories of this paper are: solv-int
19
The categories of this paper are: eess
1
The categories of this paper are: cs
27
The categories of this paper are: comp-gas
0
The categories of this paper are: hep-ph
21
The categories of this paper are: adap-org