Related papers: Toroidal embedding of Chevalley groups over $\math…

For any block of a finite group over an algebraically closed field of characteristic $2$ which has dihedral, semidihedral, or generalized quaternion defect groups, we determine explicitly the decomposition of the associated diagonal…

The existence of triangular and unitriangular factorizations has been extensively studied for untwisted Chevalley groups, as well as for twisted Chevalley groups of types other than ${}^2A_{2n} \ (n \geq 1)$. However, the case of twisted…

Toroidal Lie algebras are $n$ variable generalizations of affine Kac-Moody Lie algebras. Full toroidal Lie algebra is the semidirect product of derived Lie algebra of toroidal Lie algebra and Witt algebra, also it can be thought of…

We discuss algebraic vector bundles on smooth k-schemes X contractible from the standpoint of A^1-homotopy theory; when k = C, the smooth manifolds X(C) are contractible as topological spaces. The integral algebraic K-theory and integral…

We suggest to compactify the universal covering of the moduli space of complex structures by non-commutative spaces. The latter are described by certain categories of sheaves with connections which are flat along foliations. In the case of…

We show that the integrability obstruction of a transitive Lie algebroid coincides with the lifting obstruction of a crossed module of groupoids associated naturally with the given algebroid. Then we extend this result to general extensions…

We restrict geometric tangential equivariant complex $T^n$-bordism to torus manifolds and provide a complete combinatorial description of the appropriate non-commutative ring. We discover, using equivariant $K$-theory characteristic…

We unify problems about the equivariant geometry of symmetric quiver representation varieties, in the finite type setting, with the corresponding problems for symmetric varieties $GL(n)/K$ where $K$ is an orthogonal or symplectic group. In…

Let $P = \Bbbk[x1,x2,x3]$ be a unimodular quadratic Poisson algebra and let $G$ be a finite subgroup of the graded Poisson automorphism group of $P$. In this paper, we prove a variant of the Shephard-Todd-Chevalley theorem for $P$ and…

We study the equivariant cobordism theory of schemes for action of linear algebraic groups. We compare the equivariant cobordism theory for the action of a linear algebraic groups with similar groups for the action of tori and deduce some…

The embeddings of complex plane projective curves in the plane are a cornerstone of the topological study of algebraic varieties. In this work, we deal with the local and global aspects of these embeddings, with a special attention to its…

We present an improved version of the cyclic covering trick, which works inside the category of toroidal embeddings

Let $G$ be a simply connected Chevalley--Demazure group scheme without $SL_2$-factors. For any unital commutative ring $R$, we denote by $E(R)$ the standard elementary subgroup of $G(R)$, that is, the subgroup generated by the elementary…

For a finite group acting on a polynomial ring, the Chevalley-Shephard-Todd Theorem proves that the fixed subring is isomorphic to a polynomial ring if and only if the group is generated by pseudo-reflections. In recent years, progress was…

In this first work dedicated to the generalisation of classic algebraic geometry to non algebraically closed fields and axiomatisable classes of fields, we develop the foundations for equiresidual algebraic geometry (EQAG), i.e. algebraic…

In our previous paper, we studied the category of semifinite bundles on a proper variety defined over a field of characteristic 0. As a result, we obtained the fact that for a smooth projective curve defined over an algebraically closed…

Let $k$ be a field of characteristic $0$. We consider principal bundles over a $k$-scheme with reductive structure group (not necessarily of finite type). It is showm in particular that for $k$ algebraically closed there exists on any…

A subunit in a monoidal category is a subobject of the monoidal unit for which a canonical morphism is invertible. They correspond to open subsets of a base topological space in categories such as those of sheaves or Hilbert modules. We…

Let G be a Lie groupoid with Lie algebroid g. It is known that, unlike in the case of Lie groups, not every subalgebroid of g can be integrated by a subgroupoid of G. In this paper we study conditions on the invariant foliation defined by a…

Let $A$ be an abelian variety over a number field $K$ with good reduction outside a finite set of primes $S$. We show that if the $\ell$-torsion subgroup schemes $A[\ell^n]$ lie in a certain category of group schemes, then $A[\ell^n]$ does…