Rings of Frobenius operators
2014 ◽
Vol 157
(1)
◽
pp. 151-167
◽
Keyword(s):
AbstractLet R be a local ring of prime characteristic. We study the ring of Frobenius operators ${\mathcal F}(E)$, where E is the injective hull of the residue field of R. In particular, we examine the finite generation of ${\mathcal F}(E)$ over its degree zero component ${\mathcal F}^0(E)$, and show that ${\mathcal F}(E)$ need not be finitely generated when R is a determinantal ring; nonetheless, we obtain concrete descriptions of ${\mathcal F}(E)$ in good generality that we use, for example, to prove the discreteness of F-jumping numbers for arbitrary ideals in determinantal rings.
Keyword(s):
2016 ◽
Vol 16
(09)
◽
pp. 1750163
Keyword(s):
2021 ◽
pp. 83-91
Keyword(s):
1971 ◽
Vol 69
(1)
◽
pp. 59-70
Keyword(s):
1991 ◽
Vol 110
(3)
◽
pp. 421-429
◽
2018 ◽
Vol 17
(11)
◽
pp. 1850202
◽
Keyword(s):
Keyword(s):