Resumen de Determinant map for the prestack of Tate objects

Aron Heleodoro

• 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.