arXiv subjects

Konrad Voelkel

Publications and source records attributed to Konrad Voelkel.

2 recordsLinked to original sources

arXiv2018

Motivic Cell Structures for Spherical Varieties

In this note, we give a general method to obtain unstable motivic cell structures, following Wendt's application of the Bialynicki-Birula algebraic Morse theory. We then apply the method to spherical varieties, with special attention to the case of rank 1, to obtain unstable motivic cell structures after a finite number of $\mathbb{P}^1$-suspensions. This work is a partial derivative of the first two chapters of the author's 2016 PhD thesis.

math.KT↗

arXiv2015

On A^1-fundamental groups of isotropic reductive groups

For an isotropic reductive group G satisfying a suitable rank condition over an infinite field k, we show that the sections of the $\mathbb{A}^1$-fundamental group sheaf of G over an extension field L/k can be identified with the second group homology of G(L). For a split group G, we provide explicit loops representing all elements in the $\mathbb{A}^1$-fundamental group. Using $\mathbb{A}^1$-homotopy theory, we deduce a Steinberg relation for these explicit loops.

math.KT↗