A_inf IS INFINITE DIMENSIONAL

Author: 

Lang, J
Ludwig, J

Publication Date: 

11 May 2020

Journal: 

Journal of the Institute of Mathematics of Jussieu

Last Updated: 

2021-09-28T08:31:07.943+01:00

DOI: 

10.1017/s1474748020000201

page: 

1-7

abstract: 

<jats:p>Given a perfect valuation ring <jats:inline-formula>
<jats:alternatives>
<jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" mimetype="image" xlink:href="S1474748020000201_inline2.png" />
<jats:tex-math>$R$</jats:tex-math>
</jats:alternatives>
</jats:inline-formula> of characteristic <jats:inline-formula>
<jats:alternatives>
<jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" mimetype="image" xlink:href="S1474748020000201_inline3.png" />
<jats:tex-math>$p$</jats:tex-math>
</jats:alternatives>
</jats:inline-formula> that is complete with respect to a rank-<jats:inline-formula>
<jats:alternatives>
<jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" mimetype="image" xlink:href="S1474748020000201_inline4.png" />
<jats:tex-math>$1$</jats:tex-math>
</jats:alternatives>
</jats:inline-formula> nondiscrete valuation, we show that the ring <jats:inline-formula>
<jats:alternatives>
<jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" mimetype="image" xlink:href="S1474748020000201_inline5.png" />
<jats:tex-math>$\mathbb{A}_{\inf }$</jats:tex-math>
</jats:alternatives>
</jats:inline-formula> of Witt vectors of <jats:inline-formula>
<jats:alternatives>
<jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" mimetype="image" xlink:href="S1474748020000201_inline6.png" />
<jats:tex-math>$R$</jats:tex-math>
</jats:alternatives>
</jats:inline-formula> has infinite Krull dimension.</jats:p>

Symplectic id: 

1131104

Submitted to ORA: 

Submitted

Publication Type: 

Journal Article