Related papers: On the Burde--de Rham theorem for finitely present…

We investigate a novel geometric Iwasawa theory for $\mathbf{Z}_p$-extensions of function fields over a perfect field $k$ of characteristic $p>0$ by replacing the usual study of $p$-torsion in class groups with the study of $p$-torsion…

We begin a systematic investigation of universal norms for $p$-adic representations in higher rank Iwasawa theory. After establishing the basic properties of the module of higher rank universal norms we construct an Iwasawa-theoretic…

Provides a counterexample to a long standing conjecture of A. Adem regarding the behaviour of the integral cohomology of a p-group.

Let p be a prime. We classify finitely generated pro-p groups G which satisfy d(H) = d(G) for all open subgroups H of G. Here d(H) denotes the minimal number of topological generators for the subgroup H. Within the category of p-adic…

Let $k$ be a perfect field of characteristic $p > 0$, $W_n = W_n(k)$. For separated $k$-schemes of finite type, we explain how rigid cohomology with compact supports can be computed as the cohomology of certain de Rham-Witt complexes with…

Let $F$ be a polynomial mappping from $\mathbb{C}^n$ to $\mathbb{C}^q$ with $n>q$. We study the De Rham cohomology of its fibres and its relative cohomology groups, by introducing a special fibre $F^{-1}(\infty)$ "at infinity" and its…

The homology groups introduced by A. Brumer can be used to establish a criterion ensuring that a profinite $\mathbb{F}_p[[G]]$-module of a pro-$p$ group $G$ has projective dimension $d<\infty$ (cf. Thm. A). This criterion yields a new…

We define the notion of accessibility for a pro-$p$ group. We prove that finitely generated pro-$p$ groups are accessible given a bound on the size of their finite subgroups. We then construct a finitely generated inaccessible pro-$p$…

We prove that for every prime $p$ algebraically clean graphs of groups are virtually residually $p$-finite and cohomologically $p$-complete. We also prove that they are cohomologically good. We apply this to certain $2$-dimensional Artin…

PhD thesis concerning cohomological finiteness conditions of infinite discrete groups. Much of the material in this thesis has also appeared in arXiv:1311.7629, arXiv:1310.6262, arXiv:1311.6156, and arXiv:1207.1597.

In order to study $p$-adic \'etale cohomology of an open subvariety $U$ of a smooth proper variety $X$ over a perfect field of characteristic $p>0$, we introduce new $p$-primary torsion sheaves. It is a modification of the logarithmic de…

We define a de Rham cohomology theory for analytic varieties over a valued field $K^\flat$ of equal characteristic $p$ with coefficients in a chosen untilt of the perfection of $K^\flat$ by means of the motivic version of Scholze's tilting…

We find an example of a finite solvable group (in fact, a finite $p$-group) without any left brace structure (equiv. which is not an IYB group). Our argument is an improvement of an argument of Rump, using previous work in other areas of…

This expository paper is based on the lectures given at the program `Modular Representation Theory of Finite and $p$-adic Groups' at the National University of Singapore. We are concerned with recent results on representation theory and…

We discuss the decomposability of torsion-free abelian groups. We show that among computable groups of finite rank this property is $\Sigma^0_3$-complete. However, when we consider groups of infinite rank, it becomes $\Sigma^1_1$-complete,…

In this note, we exhibit a method to prove the Baum-Connes conjecture (with coefficients) for extensions with finite quotients of certain groups which already satisfy the Baum-Connes conjecture. Interesting examples to which this method…

We prove the Identity Theorem for pro-$p$-groups with a single defining relation giving a positive feedback to a question of Serre on the structure of relation modules. A construction of "conjurings" indicates finality of our result in a…

We give three necessary and sufficient conditions for a pro-p group to be p-adic analytic. We show that a noetherian pro-p group having finite chain length has a finite rank and conversely. We further deduce that a noetherian pro-p group…

We give proofs of de Rham comparison isomorphisms for rigid-analytic varieties, with coefficients and in families. This relies on the theory of perfectoid spaces. Another new ingredient is the pro-etale site, which makes all constructions…

We initiate the investigation of critical exponents (in degree equal to the rank) for the vanishing of L^p-cohomology of higher rank Lie groups and related manifolds. We deal with the rank 2 case and exhibit such phenomena for SL$_3$(R) and…