# Dirac geometry I: Commutative algebra

@inproceedings{Hesselholt2022DiracGI, title={Dirac geometry I: Commutative algebra}, author={Lars Hesselholt and Piotr Pstrągowski}, year={2022} }

The homotopy groups of a commutative algebra in spectra form a commutative algebra in the symmetric monoidal category of graded abelian groups. The grading and the Koszul sign rule are remnants of the structure encoded by anima as opposed to sets. The purpose of this paper and its sequel is to develop the geometry built from such algebras. We name this geometry Dirac geometry, since the grading exhibits the hallmarks of spin. Indeed, it is a reflection of the internal structure encoded by anima…

## References

SHOWING 1-10 OF 31 REFERENCES

### Realizability of algebraic galois extensions by strictly commutative ring spectra

- Mathematics
- 2004

We discuss some of the basic ideas of Galois theory for commutative S-algebras originally formulated by John Rognes. We restrict our attention to the case of finite Galois groups and to global Galois…

### Structured Ring Spectra: Moduli spaces of commutative ring spectra

- Mathematics
- 2004

Let E be a homotopy commutative ring spectrum, and suppose the ring of cooperations E∗E is flat over E∗. We wish to address the following question: given a commutative E∗-algebra A in E∗E-comodules,…

### Adams spectral sequences and Franke's algebraicity conjecture

- Mathematics
- 2021

To any well-behaved homology theory we associate a derived $\infty$-category which encodes its Adams spectral sequence. As applications, we prove a conjecture of Franke on algebraicity of certain…

### The Spectrum of an Equivariant Cohomology Ring: II

- Mathematics
- 1971

Let G be a compact Lie group (e.g., a finite group) and let HG= H*(BG, Z/pZ) be its mod p cohomology ring. One knows this ring is finitely generated, hence upon dividing out by the ideal of nilpotent…

### Filtrations on the Homology of Algebraic Varieties

- Mathematics
- 1994

Introduction Questions and speculations Abelian monoid varieties Chow varieties and Lawson homology Correspondences and Lawson homology "Multiplication" of algebraic cycles Operations in Lawson…

### Galois Extensions of Structured Ring Spectra/Stably Dualizable Groups

- Mathematics
- 2008

Galois Extensions of Structured Ring Spectra: Abstract Introduction Galois extensions in algebra Closed categories of structured module spectra Galois extensions in topology Examples of Galois…

### Commutative Ring Theory

- Mathematics
- 1989

Preface Introduction Conventions and terminology 1. Commutative rings and modules 2. prime ideals 3. Properties of extension rings 4. Valuation rings 5. Dimension theory 6. Regular sequences 7.…