Timeline for $F$-pure threshold of an $F$-pure ideal

7 events

when toggle format	what		by	license	comment
Oct 7, 2016 at 15:45	history	edited	Tom Church	CC BY-SA 3.0	deleted 7 characters in body
Oct 7, 2016 at 15:37	comment	added	lemiller		This paper has the calculation for the $F$-pure threshold which can easily fail to be $1$. I'm sure there are much easier examples however.
Oct 7, 2016 at 15:32	comment	added	Aurora		@lemiller, Thanks. Would you please mention its reference? The question can be modifies as, whether $F$-pure ideals have a particular $F$-pure threshold, something like a function of the dimension of the ring or the codimension of the defining ideal
Oct 7, 2016 at 15:29	comment	added	lemiller		The question isn't worded particularly well. What is A? The $F$-pure threshold takes as input the data of a pair $(R, \mathfrak{a})$ so I assume you are using $(A, \mathfrak{a})$ when you write $fpt(\mathfrak{a})$. There are examples of regular local rings $A$ with $F$-pure quotient $A/\mathfrak{a}$ and yet the $F$-pure threshold of the pair $(A, \mathfrak{a}) \neq 1$; an easy one that comes to mind is taking $A$ to be a polynomial ring in $n^2$ variables and $\mathfrak{a}$ the ideal defined by minors of the matrix of variables.
S Oct 7, 2016 at 14:33	history	suggested	C.F.G	CC BY-SA 3.0	improve formatting
Oct 7, 2016 at 14:20	review	Suggested edits
S Oct 7, 2016 at 14:33
Oct 7, 2016 at 12:48	history	asked	Aurora	CC BY-SA 3.0