Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Hirzebruch-Riemann-Roch for complex analytic infinity-prestacks

Cheyne Glass, Thomas Tradler, Mahmoud Zeinalian

Abstract

We provide a cocycle-level Hirzebruch-Riemann-Roch (HRR) identity for arbitrary complex analytic infinity-prestacks. We view this work as the natural setting for Toledo and Tong's HRR philosophy and technical machinery.

Hirzebruch-Riemann-Roch for complex analytic infinity-prestacks

Abstract

We provide a cocycle-level Hirzebruch-Riemann-Roch (HRR) identity for arbitrary complex analytic infinity-prestacks. We view this work as the natural setting for Toledo and Tong's HRR philosophy and technical machinery.
Paper Structure (7 sections, 17 theorems, 40 equations)

This paper contains 7 sections, 17 theorems, 40 equations.

Table of Contents

  1. $\infty$-(pre)stacks on $\text{St}\mathbb{C}^n$
  2. An $\infty$-stack of charts
  3. Two $\infty$-prestacks of forms
  4. Toledo and Tong's Čech parametrix as a map of $\infty$-prestacks
  5. Invariant polynomials
  6. Evaluating $\infty$-stacks on $G$-Manifolds
  7. Applications

Key Result

Lemma 1.3

The collection $\text{Cov}(\text{St}\mathbb{C}^n)$ provides a Verdier site structure on $\text{St}\mathbb{C}^n$ .

Theorems & Definitions (57)

  • Definition 1.1
  • Definition 1.2
  • Lemma 1.3
  • proof
  • Definition 1.4
  • Definition 1.5
  • Definition 1.6
  • Proposition 1.7
  • proof
  • Definition 2.1
  • ...and 47 more