Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Betti tables of $p$-Borel-fixed ideals   In this note we provide a counter-example to a conjecture of K. Pardue
[Thesis, Brandeis University, 1994.], which asserts that if a monomial ideal is
$p$-Borel-fixed, then its $\naturals$-graded Betti table, after passing to any
field does not depend on the field. More precisely, we show that, for any
monomial ideal $I$ in a polynomial ring $S$ over the ring $\ints$ of integers
and for any prime number $p$, there is a $p$-Borel-fixed monomial $S$-ideal $J$
such that a region of the multigraded Betti table of $J(S \otimes_\ints \ell)$
is in one-to-one correspondence with the multigraded Betti table of $I(S
\otimes_\ints \ell)$ for all fields $\ell$ of arbitrary characteristic. There
is no analogous statement for Borel-fixed ideals in characteristic zero.
Additionally, the construction also shows that there are $p$-Borel-fixed ideals
with non-cellular minimal resolutions.

6
The categories of this paper are: astro-ph
36
The categories of this paper are: cmp-lg
32
The categories of this paper are: atom-ph
3
The categories of this paper are: physics
27
The categories of this paper are: comp-gas
15
The categories of this paper are: nucl-ex
17
The categories of this paper are: q-fin
37
The categories of this paper are: supr-con
35
The categories of this paper are: mtrl-th
10
The categories of this paper are: q-bio
13
The categories of this paper are: quant-ph
33
The categories of this paper are: plasm-ph
30
The categories of this paper are: q-alg
14
The categories of this paper are: math-ph
18
The categories of this paper are: econ
0
The categories of this paper are: hep-ph