Mar

31

Chris Kapulkin

Mar 31, 14:30 - 15:30

MC 107

Cryptographic Multilinear Maps

Apr

07

Tristan Freiberg

Apr 07, 14:30 - 15:30

MC 107

TBA

Apr

12

Vaidehee Thatte

Apr 12, 14:30 - 16:0

MC 108

Ramification theory for arbitrary valuation rings in positive characteristic

Our goal is to develop ramification theory for arbitrary valuation fields, that is compatible with the
classical theory of complete discrete valuation fields with perfect residue fields. We consider fields
with more general (possibly non-discrete) valuations and arbitrary (possibly imperfect) residue
fields. The defect case, i.e., the case where there is no extension of either the residue field or the
value group, gives rise to many interesting complications. We present some new results for Artin-
Schreier extensions of valuation fields in positive characteristic. These results relate the "higher
ramification ideal" of the extension with the ideal generated by the inverses of Artin-Schreier
generators via the norm map. We also introduce a generalization and further refinement of Kato's
refined Swan conductor in this case. Similar results are true in the mixed characteristic case.