Vol. 7, No. 1, 2022

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The motivic Segal–Becker theorem for algebraic K-theory

Roy Joshua and Pablo Pelaez

Vol. 7 (2022), No. 1, 191–221
Abstract

The present paper is a continuation of earlier work by Gunnar Carlsson and the first author on a motivic variant of the classical Becker–Gottlieb transfer and an additivity theorem for such a transfer by the present authors. Here, we establish a motivic variant of the classical Segal–Becker theorem relating the classifying space of a 1-dimensional torus with the spectrum defining algebraic K-theory.

Keywords
motivic Becker–Gottlieb transfer, motivic Segal–Becker theorem
Mathematical Subject Classification
Primary: 14F42, 19E08
Milestones
Received: 5 July 2021
Revised: 19 December 2021
Accepted: 7 January 2022
Published: 20 June 2022
Authors
Roy Joshua
Department of Mathematics
Ohio State University
Columbus, OH
United States
Pablo Pelaez
Instituto de Matemáticas
IMATE, UNAM
Area de la Investigacion Cientifica
Circuito Exterior, Ciudad Universitaria
Ciudad de México
Mexico