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On mod 2 arith- metic Dijkgraaf-Witten invariants for certain real quadratic number fields

Hold Date 2020-01-31 16:00~2020-01-31 17:00

Place Lecture Room M W1-C-513, West Zone 1, Ito campus, Kyushu University

Object person  

Speaker Hikaru HIRANO (Kyushu university)

In recent years, based on the analogies in arithmetic topology, Minhyong Kim initiated to study arithmetic Chern-Simons theory, and introduced an arithmetic analogy for totally imaginary number fields of the Dijkgraaf-Witten invariants for 3-manifolds. In this talk, we extend Kim’s definition for any number field, by using the modified etale cohomology groups which take real places into account. We then show explicit formulas of mod 2 arithmetic Chern-Simons and Dijkgraaf-Witten invariants for certain real quadratic fields. We also show a topological analogue of our results.