Related papers: Smooth profinite groups, II: the Uplifting Pattern

Matroid bundles, introduced by MacPherson, are combinatorial analogues of real vector bundles. This paper sets up the foundations of matroid bundles, and defines a natural transformation from isomorphism classes of real vector bundles to…

Ensemble learning is traditionally justified as a variance-reduction strategy, explaining its strong performance for unstable predictors such as decision trees. This explanation, however, does not account for ensembles constructed from…

I categorify the definition of fibre bundle, replacing smooth manifolds with differentiable categories, Lie groups with coherent Lie 2-groups, and bundles with a suitable notion of 2-bundle. To link this with previous work, I show that…

We prove that the category of profinite cosheaves valued in a pro-regular category (satisfying mild assumptions) is itself a pro-regular category. As a corollary, we extend Wilkes's cosheaf-bundle equivalence from profinite modules to…

We develop the theory of Mackey profunctors, a version of Mackey functors for profinite groups.

We consider a family of Levi-degenerate finite type hypersurfaces in $\mathbb C^2$, where in general there is no group structure. We lift these domains to stratified Lie groups via a constructive proof, which optimizes the well-known…

In this paper, we generalise the construction of the functorial pullback of refined unramified cohomology between smooth schemes, by following the ideas of Fulton's intersection theory and Rost's cycle modules. We also define standard…

A smooth scheme X over a field k of positive characteristic is said to be strongly liftable, if X and all prime divisors on X can be lifted simultaneously over W_2(k). In this paper, first we prove that smooth toric varieties are strongly…

We prove that every smooth affine variety of dimension $d$ embeds into every simple algebraic group of dimension at least $2d+2$. We do this by establishing the existence of embeddings of smooth affine varieties into the total space of…

First we survey and explain the strategy of some recent results that construct holomorphic $\text{sl}(2, \mathbb C)$-differential systems over some Riemann surfaces $\Sigma_g$ of genus $g\geq 2$, satisfying the condition that the image of…

If $\mathcal E, \mathcal F$ are vector bundles of ranks $r-1,r$ on a smooth fourfold $X$ and $\mathcal{Hom}(\mathcal E,\mathcal F)$ is globally generated, it is well known that the general map $\phi: \mathcal E \to \mathcal F$ is injective…

We show that the covolume of an irreducible lattice in a higher rank semisimple Lie group with the congruence subgroup property is determined by the profinite completion. Without relying on CSP, we additionally show that volume is a…

The main aim of this article is to give new classes of smooth projective varieties over characteristic $p>0$ that admit flat liftings over the Witt vectors together with additional data (logarithmic structure and the Frobenius morphism) by…

In this work, we study topological properties of surface bundles, with an emphasis on surface bundles with a spin structure. We develop a criterion to decide whether a given manifold bundle has a spin structure and specialize it to surface…

Finite \'etale covers of a connected scheme $X$ are parametrised by the \'etale fundamental group via the monodromy correspondence. This was generalised to an exodromy correspondence for constructible sheaves, first in the topological…

We provide a uniform construction of "mixed versions" or "graded lifts" in the sense of Beilinson-Ginzburg-Soergel which works for arbitrary Artin stacks. In particular, we obtain a general construction of graded lifts of many categories…

We introduce an extension of the (tame) polynomial automorphism group over finite fields: the profinite (tame) polynomial automorphism group, which is obtained by putting a natural topology on the automorphism group. We show that most known…

A group $\Gamma$ has separable cohomology if the profinite completion map $\iota \colon \Gamma \to \widehat{\Gamma}$ induces an isomorphism on cohomology with finite coefficient modules. In this article, cohomological separability is…

In this paper, we introduce a symmetric continuous cohomology of topological groups. This is obtained by topologizing a recent construction due to Staic (J. Algebra 322 (2009), 1360-1378), where a symmetric cohomology of abstract groups is…

One of the major advantages of $\infty$-category theory over classical $1$-category theory is its robust and homotopically meaningful framework for taking (co)limits of diagrams of $\infty$-categories. However, it is both subtle and crucial…