On the normally ordered tensor product and duality for Tate objects

O. Braunling, M. Groechenig, A. Heleodoro, J. Wolfson

This paper generalizes the normally ordered tensor product from Tate vector spaces to Tate objects over arbitrary exact categories. We show how to lift bi-right exact monoidal structures, duality functors, and construct external Homs. We list some applications: (1) Adeles of a flag can be written as ordered tensor products; (2) Intersection numbers can be interpreted via these tensor products; (3) Pontryagin duality uniquely extends to n-Tate objects in locally compact abelian groups.

Keywords: Tate vector space, Tate object, normally ordered product, higher adeles,higher local fields

2010 MSC: 14A22, 18B30

Theory and Applications of Categories, Vol. 33, 2018, No. 13, pp 296-349.

A corrigendum is published as Theory and Applications of Categories, Vol. 39, 2023, No. 7, pp 186-188.