## 5 Citations

Homotopy Rational Points of Brauer-Severi Varieties

- Mathematics
- 2015

We study homotopy rational points of Brauer-Severi varieties over fields of characteristic zero. We are particularly interested if a Brauer-Severi variety admitting a homotopy rational point splits.…

Brauer and Etale Homotopy Obstructions to Rational Points on Open Covers

- Mathematics
- 2020

In 2010, Poonen gave the first example of failure of the local-global principle that cannot be explained by Skorobogatov's etale Brauer-Manin obstruction. Motivated by this example, we show that the…

Obstructions to rational and integral points

- Mathematics
- 2018

In this thesis, I study two examples of obstructions to rational and integral points on varieties. The first concerns the S-unit equation, which asks for solutions to x+ y = 1 with x and y both…

BRAUER AND ETALE HOMOTOPY OBSTRUCTIONS ON OPEN COVERS

- 2020

The Brauer-Manin obstruction can be used to explain the failure of the local-global principle for many algebraic varieties. In 1999, Skorobogatov gave the first example of a variety whose failure to…

Homotopy Spectra and Diophantine Equations

- Mathematics
- 2020

Arguably, the first bridge between vast, ancient, but disjoint domains of mathematical knowledge, – topology and number theory, – was built only during the last fifty years. This bridge is the theory…

## References

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The real section conjecture and Smith's fixed-point theorem for pro-spaces

- Mathematics, Computer ScienceJ. Lond. Math. Soc.
- 2011

We prove a topological version of the section conjecture for the profinite completion of the fundamental group of finite CW-complexes equipped with the action of a group of prime order $p$ whose…

Étale homotopy equivalence of rational points on algebraic varieties

- Mathematics
- 2015

It is possible to talk about the \'etale homotopy equivalence of rational points on algebraic varieties by using a relative version of the \'etale homotopy type. We show that over $p$-adic fields…

Rational points, $R$-equivalence and \'etale homotopy of algebraic varieties

- Mathematics
- 2010

We study a generalisation of the anabelian section conjecture of Grothendieck by substituting the arithmetic fundamental group with a relative version of the étale homotopy type. We show that the map…

CONTINUOUS HOMOTOPY FIXED POINTS FOR LUBIN-TATE SPECTRA

- Mathematics
- 2009

We provide a new and conceptually simplified construction of continuous homotopy fixed point spectra for Lubin-Tate spectra under the action of the extended Morava stabilizer group. Moreover, our new…

PROFINITE G-SPECTRA

- Mathematics
- 2013

We construct a stable model structure on profinite spectra with a continuous action of an arbitrary profinite group. The motivation is to provide a natural framework in a subsequent paper for a new…

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…

Equivariant stable homotopy and Sullivan's conjecture

- Mathematics
- 1991

Let G be a p-group, and let X be a G-complex. Let EG denote a contractible space on which G acts freely. By the "homotopy fixed point set" of X, we mean the fixed point set F(EG, X) G, where F(EG, X)…

SOME REMARKS ON PROFINITE COMPLETION OF SPACES

- Mathematics
- 2011

We study profinite completion of spaces in the model category of profinite spaces and construct a rigidification of the completion functors of Artin-Mazur and Sullivan which extends also to…