Skip to main content
MathOverflow

Return to Question

minor TeX improvements
Source Link
edit approved Nov 22, 2013 at 10:49
Sergiy Kozerenko
edit approved Nov 22, 2013 at 10:49
Sergiy Kozerenko
  • 747
  • 1
  • 7
  • 17

Let's say I have a field k$\mathbb{K}$ and a flat family of k[t]$\mathbb{K}[t]$-modules M$M$ over the formal disk Spec k[[h]]$Spec \mathbb{K}[[h]]$.

Now, assume that M/hM$M/hM$ is torsion as a k[t]$\mathbb{K}[t]$-module (but NOT finitely generated). Can I conclude that M[h^{-1}]$M[h^{-1}]$ is torsion as a k((h))[t] module$\mathbb{K}((h))[t]$-module?

Let's say I have a field k and a flat family of k[t]-modules M over the formal disk Spec k[[h]].

Now, assume that M/hM is torsion as a k[t]-module (but NOT finitely generated). Can I conclude that M[h^{-1}] is torsion as a k((h))[t] module?

Let's say I have a field $\mathbb{K}$ and a flat family of $\mathbb{K}[t]$-modules $M$ over the formal disk $Spec \mathbb{K}[[h]]$.

Now, assume that $M/hM$ is torsion as a $\mathbb{K}[t]$-module (but NOT finitely generated). Can I conclude that $M[h^{-1}]$ is torsion as a $\mathbb{K}((h))[t]$-module?

Bounty Ended with Ian Shipman's answer chosen by Ben Webster♦
Bounty Started worth 50 reputation by Ben Webster♦
deleted 1 characters in body
Source Link
Ben Webster ♦
Ben Webster ♦
  • 44.7k
  • 12
  • 126
  • 260

Let's say I have a field k and a flat family of k[t]-modules M over the diskformal disk Spec k[h]k[[h]].

Now, assume that M/hM is torsion as a k[t]-module (but NOT finitely generated). Can I conclude that M/(hM[h^{-i)M1}] is torsion as a k[t] module for any i in k((h))[t] module?

Let's say I have a field k and a flat family of k[t]-modules M over the disk Spec k[h].

Now, assume that M/hM is torsion as a k[t]-module (but NOT finitely generated). Can I conclude that M/(h-i)M is torsion as a k[t] module for any i in k?

Let's say I have a field k and a flat family of k[t]-modules M over the formal disk Spec k[[h]].

Now, assume that M/hM is torsion as a k[t]-module (but NOT finitely generated). Can I conclude that M[h^{-1}] is torsion as a k((h))[t] module?

Source Link
Ben Webster ♦
Ben Webster ♦
  • 44.7k
  • 12
  • 126
  • 260

are deformations of torsion modules always torsion?

Let's say I have a field k and a flat family of k[t]-modules M over the disk Spec k[h].

Now, assume that M/hM is torsion as a k[t]-module (but NOT finitely generated). Can I conclude that M/(h-i)M is torsion as a k[t] module for any i in k?