Determinant map for the prestack of Tate objects
Abstract
We construct a map from the prestack of Tate objects over a commutative ring $k$ to the stack of $\mathbb{G}_{\rm m}$gerbes. The result is obtained by combining the determinant map from the stack of perfect complexes as proposed by SchürgToënVezzosi with a relative $S_{\bullet}$construction for Tate objects as studied by BraunlingGroechenigWolfson. Along the way we prove a result about the Ktheory of vector bundles over a connective $\mathbb{E}_{\infty}$ring spectrum which is possibly of independent interest.
 Publication:

arXiv eprints
 Pub Date:
 June 2019
 DOI:
 10.48550/arXiv.1907.00384
 arXiv:
 arXiv:1907.00384
 Bibcode:
 2019arXiv190700384H
 Keywords:

 Mathematics  Algebraic Geometry;
 Mathematics  KTheory and Homology;
 14;
 19
 EPrint:
 Section 2 rewritten, some results now hold more generally