Algebraic K-theory, A^1-homotopy and Riemann-Roch theorems

TL;DR

This paper explores the intersection of algebraic K-theory, A^1-homotopy theory, and Riemann-Roch theorems, revealing new insights into higher algebraic K-theory and related operations.

Contribution

It introduces a framework combining SGA 6 constructions with A^1-homotopy theory to derive results on higher algebraic K-theory, Chern characters, and Riemann-Roch theorems.

Findings

Establishes a natural link between SGA 6 constructions and A^1-homotopy theory

Derives new results on higher algebraic K-theory operations

Provides a homotopy-theoretic approach to Riemann-Roch theorems

Abstract

In this article, we show that the combination of the constructions done in SGA 6 and the A^1-homotopy theory naturally leads to results on higher algebraic K-theory. This applies to the operations on algebraic K-theory, Chern characters and Riemann-Roch theorems.