arXiv subjects

Thomas Poguntke

Publications and source records attributed to Thomas Poguntke.

3 recordsLinked to original sources

arXiv2018

Equivariant motivic Hall algebras

We introduce a generalization of Joyce's motivic Hall algebra by combining it with Green's parabolic induction product, as well as a non-archimedean variant of it. In the construction, we follow Dyckerhoff-Kapranov's formalism of 2-Segal objects and their transferred algebra structures. Our main result is the existence of an integration map under any suitable transfer theory, of course including the (analytic) equivariant motivic one. This allows us to study Harder-Narasimhan recursion formulas in new cases.

math.AG↗

arXiv2018

Group Schemes with $\mathbb F_q$-Action

Via a construction due to V. Drinfel'd, we prove an equivalence of categories, generalizing the equivalence between commutative flat group schemes in characteristic $p$ with trivial Verschiebung and their Dieudonné modules to group schemes with $\mathbb F_q$-action.

math.AG↗

arXiv2017

Higher Segal structures in algebraic $K$-theory

We introduce higher dimensional analogues of simplicial constructions due to Segal and Waldhausen, respectively producing the direct sum and algebraic $K$-theory spectra of an exact category. We then investigate their fibrancy properties, based on the formalism of higher Segal spaces by Dyckerhoff-Kapranov.

math.AT↗