## Algebra

•  Vaidehee Thatte, SUNY Binghamton
•  Arbitrary Valuation Rings and Wild Ramification
•  01/27/2021
•  4:00 PM - 5:00 PM
•  Online (virtual meeting) (Virtual Meeting Link)
•  Preston Wake (wakepres@msu.edu)

We aim to develop ramification theory for arbitrary valuation fields, extending the classical theory of complete discrete valuation fields with perfect residue fields. By studying wild ramification, we hope to understand the mysterious phenomenon of the $\textit{defect}$ (or ramification deficiency) unique to the positive residue characteristic case and is one of the main obstacles in obtaining resolution of singularities. Extensions of degree $p$ in residue characteristic $p>0$ are building blocks of the general case. We present a generalization of ramification invariants for such extensions. These results enable us to construct an upper ramification filtration of the absolute Galois group of Henselian valuation fields (joint with K.Kato).

## Contact

Department of Mathematics
Michigan State University