Tambara Functors on Profinite Groups and Generalized Burnside Functors

Abstract

The Tambara functor was defined by Tambara in the name of TNR-functor, to treat certain ring-valued Mackey functors on a finite group. Recently Brun revealed the importance of Tambara functors in the Witt–Burnside construction. In this article, we define the Tambara functor on the Mackey system of Bley and Boltje. Yoshida's generalized Burnside ring functor is the first example. Consequently, we can consider a Tambara functor on any profinite group. In relation with the Witt–Burnside construction, we can give a Tambara-functor structure on Elliott's functor V _M , which generalizes the completed Burnside ring functor of Dress and Siebeneicher.

Key Words:

• Mackey functor
• Tambara functor
• Witt–Burnside ring

2000 Mathematics Subject Classification:

• Primary 19A22
• Secondary 18B40, 20J05

ACKNOWLEDGMENTS

The author wishes to thank Professor Toshiyuki Katsura for his encouragement. The author is supported by JSPS.

Notes

Communicated by D. K. Nakano.