# Homotopy invariance of tame homotopy groups of regular schemes

@inproceedings{Schmidt2021HomotopyIO, title={Homotopy invariance of tame homotopy groups of regular schemes}, author={Alexander Schmidt}, year={2021} }

The étale homotopy groups of schemes as defined by Artin and Mazur [AM69] have the disadvantage of being homotopy invariant only in characteristic zero. This and other related problems led to the definition of the tame topology which is coarser than the étale topology by disallowing wild ramification along the boundary of compactifications, see [HS21]. The objective of this paper is to show that the associated tame homotopy groups are indeed (A-)homotopy invariant, at least for regular schemes.

## References

SHOWING 1-10 OF 33 REFERENCES

### The tame site of a scheme

- MathematicsInventiones mathematicae
- 2020

Etale cohomology with non-invertible coefficients has some unpleasant properties, e.g., it is not A^1-homotopy invariant and for constructible coefficients the expected finiteness properties do not…

### Etale Homotopy of Simplicial Schemes.

- Mathematics
- 1982

This book presents a coherent account of the current status of etale homotopy theory, a topological theory introduced into abstract algebraic geometry by M. Artin and B. Mazur. Eric M. Friedlander…

### Motivic aspects of anabelian geometry

- Mathematics
- 2012

We discuss the role which might be played in anabelian geometry by the ´ homotopy type of Artin and Mazur. We quote some results around the question how local the construction is. Furthermore, we…

### Tame Class Field Theory for Singular Varieties over Algebraically Closed Fields

- Mathematics
- 2016

Let X be a separated scheme of finite type over an algebraically closed field k and let m be a natural number. By an explicit geometric construction using torsors we construct a pairing between the…

### On different notions of tameness in arithmetic geometry

- Mathematics
- 2008

The notion of a tamely ramified covering is canonical only for curves. Several notions of tameness for coverings of higher dimensional schemes have been used in the literature. We show that all these…

### Algebraic Geometry and Arithmetic Curves

- Mathematics
- 2002

Introduction 1. Some topics in commutative algebra 2. General Properties of schemes 3. Morphisms and base change 4. Some local properties 5. Coherent sheaves and Cech cohmology 6. Sheaves of…

### Local Uniformization on Algebraic Varieties

- Mathematics
- 1940

1. In [10] (p. 650) we have proved a uniformization theorem for zero-dimensional valuations on an algebraic surface, over an algebraically closed ground field K (of characteristic zero). In the…

### On quasi-purity of the branch locus

- Mathematicsmanuscripta mathematica
- 2018

Let k be a field, K/k finitely generated and L/K a finite, separable extension. We show that the existence of a k-valuation on L which ramifies in L/K implies the existence of a normal model X of K…