Related papers: Reducedness of twisted loop groups

We give a complete classsification of reduced sextics of torus type with configurations of the singularities and the geometry of the components.

We generalize the notion of Ekedahl-Oort strata to elements in the loop group of any connected reductive group, and call the resulting discrete invariant the truncation of level 1 of the element. We give conditions for the Newton points…

We give an elementary proof to Hasse theorem.

We prove the vanishing of certain low degree cohomologies of some induced representations. As an application, we determine certain low degree cohomologies of congruence groups.

We categorify a quantized Heisenberg algebra associated to a finite subgroup of SL(2,C).

The note provides a simple proof of Kisin's theorem about the restriction of crystalline representations to certain subgroup of the Galois group.

The recent proof by Bigelow and Krammer that the braid groups are linear opens the possibility of applications to the study of knots and links. It was proved by the first author and Menasco that any closed braid representative of the unknot…

We prove Hida-style control theorems in the derived setting for a large class of reductive groups tailored for applications to Euler systems.

We prove the existence of an algorithm which solves the reducibility problem in braid groups and runs in quadratic time with respect to the braid length for any fixed braid index.

We prove several generalisations of the ping-pong lemma for negatively curved groups.

We introduce a delooping model of relative exact categories. It gives us a condition that the negative K-group of a relative exact category becomes trivial.

We study and give examples of braided groupoids, and, a fortiori, non-degenerate solutions of the quiver-theoretical braid equation.

The main result of this paper (Theorem B) asserts that under natural conditions, any weakly-split Tits system in G(k), G a reductive or quasi-reductive group over an arbitrary field k, is the standard one.

In this article we investigate the question of finding a network configuration of minimal length connecting three given points in the Heisenberg group. After proving existence of (possibly degenerate) minimal horizontal triods, we…

Similarly to how the classical group ring isomorphism problem asks, for a commutative ring $R$, which information about a finite group $G$ is encoded in the group ring $RG$, the twisted group ring isomorphism problem asks which information…

We expose a rather simple and direct approach to the structure theory of prime PI-rings ("Posner's theorem"), based on fundamental properties of the extended centroid of a prime ring.

For any knot, the following are equivalent. (1) The infinite cyclic cover has uncountably many finite covers; (2) there exists a finite-image representation of the knot group for which the twisted Alexander polynomial vanishes; (3) the knot…

In this article, we propose a boundedness conjecture for the regional fundamental group of klt singularities. We prove that this boundedness conjecture, the Zariski closedness of the diminished base locus of $K_X$, and an upper bound for…

We develop a theory of type semigroups for arbitrary twisted, not necessarily Hausdorff \'etale groupoids. The type semigroup is a dynamical version of the Cuntz semigroup. We relate it to traces, ideals, pure infiniteness, and stable…

We give the construction of twisted quantum Lax equations associated with quantum groups. We solve these equations using factorization properties of the corresponding quantum groups. Our construction generalizes in many respects the…