Determinant map for the prestack of Tate objects

Aron Heleodoro ^[1]
1. [1] University of Illinois at Urbana–Champaign, USA
Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 26, Nº. 5, 2020
Idioma: inglés
DOI: 10.1007/s00029-020-00604-3
Enlaces
- Texto completo
Resumen
- We construct a map from the prestack of Tate objects over a commutative ring k to the stack of {\mathbb {G}}_{\mathrm{m}}-gerbes. The result is obtained by combining the determinant map from the stack of perfect complexes as proposed by Schürg–Toën–Vezzosi with a relative S_{\bullet }-construction for Tate objects as studied by Braunling–Groechenig–Wolfson. Along the way we prove a result about the K-theory of vector bundles over a connective {\mathbb {E}}_{\infty }-ring spectrum which is possibly of independent interest.