NTS ABSTRACTSpring2024: Difference between revisions
Smarshall3 (talk | contribs) (Created page with " Back to the number theory seminar main webpage: [https://www.math.wisc.edu/wiki/index.php/NTS Main page]") |
Smarshall3 (talk | contribs) No edit summary |
||
| Line 1: | Line 1: | ||
Back to the number theory seminar main webpage: [https://www.math.wisc.edu/wiki/index.php/NTS Main page] | Back to the number theory seminar main webpage: [https://www.math.wisc.edu/wiki/index.php/NTS Main page] | ||
== Jan 25 == | |||
<center> | |||
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20" | |||
|- | |||
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Jason Kountouridis''' | |||
|- | |||
| bgcolor="#BCD2EE" align="center" | The monodromy of simple surface singularities in mixed characteristic | |||
|- | |||
| bgcolor="#BCD2EE" | | |||
Given a smooth proper surface X over a $p$-adic field, it is a generally open problem in arithmetic geometry to relate the mod $p$ reduction of X with the monodromy action of inertia on the $\ell$-adic cohomology of X, the latter viewed as a Galois representation ($\ell \neq p$). In this talk, I will focus on the case of X degenerating to a surface with simple singularities, also known as rational double points. This class of singularities is linked to simple simply-laced Lie algebras, and in turn this allows for a concrete description of the associated local monodromy. Along the way we will see how Springer theory enters the picture, and we will discuss a mixed-characteristic version of some classical results of Artin, Brieskorn and Slodowy on simultaneous resolutions. | |||
|} | |||
</center> | |||
<br> | |||
Revision as of 21:22, 13 January 2024
Back to the number theory seminar main webpage: Main page
Jan 25
| Jason Kountouridis |
| The monodromy of simple surface singularities in mixed characteristic |
|
Given a smooth proper surface X over a $p$-adic field, it is a generally open problem in arithmetic geometry to relate the mod $p$ reduction of X with the monodromy action of inertia on the $\ell$-adic cohomology of X, the latter viewed as a Galois representation ($\ell \neq p$). In this talk, I will focus on the case of X degenerating to a surface with simple singularities, also known as rational double points. This class of singularities is linked to simple simply-laced Lie algebras, and in turn this allows for a concrete description of the associated local monodromy. Along the way we will see how Springer theory enters the picture, and we will discuss a mixed-characteristic version of some classical results of Artin, Brieskorn and Slodowy on simultaneous resolutions. |