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April 19, 2024Open Access

Equivariant Algebraic K-Theory and Derived completions III: Applications

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Authors

GCGunnar CarlssonRJRoy Joshua⋆PPPablo Pelaez

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Overview

Theoretical analysis demonstrates generalized Riemann-Roch theorems for equivariant G-theory across normal quasi-projective schemes, highlighting broader computational frameworks.

Key Points

  • Derived completion theorems establish general Riemann-Roch formulations for equivariant G-theory and equivariant homotopy K-theory across normal quasi-projective schemes.
  • Riemann-Roch and Lefschetz-Riemann-Roch theorems apply directly to all toric and spherical varieties under actions of linear algebraic and diagonalizable group schemes.
  • Theoretical framework constructs spectral sequences computing the homotopy groups of derived completions of equivariant G-theory via Borel-Moore motivic cohomology.

Cite This Study

Carlsson et al. (2024) studied this question.

synapsesocial.com/papers/68e6e76cb6db643587663141https://doi.org/10.48550/arxiv.2404.13199
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  1. 1Equivariant Algebraic K-Theory and Derived completions II: the case of Equivariant Homotopy K-Theory and Equivariant K-Theory2024
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  5. 5Derived Equivalence for Elliptic K3 Surfaces and Jacobians2024 · 1 citations