Irakli Patchkoria

activity

20092026

most citedOn the Algebraic Classification of Module Spectra

14 citations · 73 across the 19 of their papers we have counts for

collaborators

26 papers

math.AT2026

Chromatic Euler characteristics and duality for infinite groups

Gijs Heuts, Irakli Patchkoria

We study a family of generalizations of the notion of Euler characteristic of discrete groups (or of orbifolds, depending on one's perspective) indexed on the natural numbers. For…

math.AT2025

On the Farrell--Tate $K$ -theory of $Out (F_{n})$

Naomi Andrew, Irakli Patchkoria

Using Lück's Chern character isomorphism we obtain a general formula in terms of centralisers for the $p$ -adic Farrell--Tate $K$ -theory of any discrete group $G$ with a finite clas…

math.AT2024

Character theory and Euler characteristic for orbispaces and infinite groups

Wolfgang Lück, Irakli Patchkoria, Stefan Schwede

Given a discrete group $G$ with a finite model for $E G$ , we study $K (n)^{*} (B G)$ and $E^{*} (B G)$ , where $K (n)$ is the $n$ -th Morava $K$ -theory for a given prime and $E$ is…

math.AT2024

Chromatic congruences and Bernoulli numbers

Irakli Patchkoria

For every natural number $n$ and a fixed prime $p$ , we prove a new congruence for the orbifold Euler characteristic of a group. The $p$ -adic limit of these congruences as $n$ tends…

math.AT2023

Witt vectors with coefficients and TR

Emanuele Dotto, Achim Krause, Thomas Nikolaus +1

We give a new construction of $p$ -typical Witt vectors with coefficients in terms of ghost maps and show that this construction is isomorphic to the one defined in terms of formal…

math.AT2023

On the cyclic homology of certain universal differential graded algebras

Christopher Davis, Julius Frank, Irakli Patchkoria

Let $p$ be an odd prime and $R$ a $p$ -torsion-free commutative $Z_{(p)}$ -algebra. We compute the periodic cyclic homology over $R$ of the universal differential graded alg…