arXiv subjects

Yonatan Harpaz

Publications and source records attributed to Yonatan Harpaz.

39 records · Page 3Linked to original sources

arXiv2012

The Cobordism Hypothesis in Dimension 1

In 2009 Lurie published an expository article outlining a proof for a higher version of the cobordism hypothesis conjectured by Baez and Dolan in 1995. In this note we give a proof for the 1-dimensional case of this conjecture. The proof follows most of the outline given in Lurie's paper, but differs in a few crucial details. In particular, the proof makes use of the theory of quasi-unital $\infty$-categories as developed by the author in a previous note.

math.AT↗

arXiv2011

The Étale Homotopy Type and Obstructions to the Local-Global Principle

In 1969 Artin and Mazur defined the étale homotopy type of an algebraic variety \cite{AMa69}. In this paper we define various obstructions to the local-global principle on a variety $X$ over a global field using the étale homotopy type of $X$ and the concept of homotopy fixed points. We investigate relations between those "homotopy obstructions" and connect them to various known obstructions such as the Brauer -Manin obstruction, the étale-Brauer obstruction and finite descent obstructions. This gives a reinterpretation of known arithmetic obstructions in terms of homotopy theory.

math.AG↗

arXiv2011

Homotopy Obstructions to Rational Points

In this paper we propose to use a relative variant of the notion of the étale homotopy type of an algebraic variety in order to study the existence of rational points on it. In particular, we use an appropriate notion of homotopy fixed points in order to construct obstructions to the local-global principle. The main results in this paper are the connections between these obstructions and the classical obstructions, such as the Brauer-Manin, the étale-Brauer and certain descent obstructions. These connections allow one to understand the various classical obstructions in a unified framework.

math.AG↗