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We show that if X is a toric scheme over a regular ring containing a field then the direct limit of the K-groups of X taken over any infinite sequence of nontrivial dilations is homotopy invariant. This theorem was known in characteristic…

We give a detailed description of the algebraic group Aut(g) of automorphisms of a simple finite dimensional Lie superalgebra g over an algebraically closed field k of characteristic 0. We also give a description of the group of…

In this work, we establish certain enrichments of dual algebraic structures in the setting of monoidal double categories. In more detail, we obtain a tensored and cotensored enrichment of monads in comonads, as well as a tensored and…

Let $R$ be a discrete valuation ring of field of fractions $K$ and of residue field $k$ of characteristic $p > 0$. In an earlier work, we studied the question of extending torsors on $K$-curves into torsors over $R$-regular models of the…

The main goal of the present paper is two-fold. First we extend the theory of toroidal embeddings introduced by Kempf, Knudsen, Mumford and Saint-Donat to the class of toroidal varieties with stratifications (which is the main body of the…

Kuratowski's closure-complement problem gives rise to a monoid generated by the closure and complement operations. Consideration of this monoid yielded an interesting classification of topological spaces, and subsequent decades saw further…

We revisit the transformation rules of the metric and Kalb-Ramond field under T-duality, and express the corresponding relations in terms of the metric G and the field strength H=dB. In the course of the derivation, we find an explanation…

We show that, for a complete simplicial toric variety $X$, we can determine its homotopy $\KH$-theory entirely in terms of the torus pieces of open sets forming an open cover of $X$. We then construct conditions under which, given two…

Working over a field $k$ of characteristic zero, this paper studies algebraic actions of $SL_2(k)$ on affine $k$-domains by defining and investigating fundamental pairs of derivations. There are three main results: (1) The Structure Theorem…

Under mild assumptions, we characterise modules with projective resolutions of length n in the target category of filtrated K-theory over a finite topological space in terms of two conditions involving certain Tor-groups. We show that the…

Let $R$ and $S$ be rings and $_R\omega_S$ a semidualizing bimodule. We study when the double functor $\Tor^S_i(\omega, \Ext^i_{R}(\omega,-))$ preserves epimorphisms and the double functor $\Ext_{R}^i(\omega, \Tor_i^{S}(\omega,-))$ preserves…

Let $\cal R$ be either the Grothendieck semiring (semiring with multiplication) of complex algebraic varieties, or the Grothendieck ring of these varieties, or the Grothendieck ring localized by the class of the complex affine line. We…

The Wronskian determinants (for coefficients of higher-order differential operators on the affine real line or circle) satisfy the table of Jacobi-type quadratic identities for strong homotopy Lie algebras -- i.e. for a particular case of…

We construct chiral algebras that centralize rank-two Nichols algebras with at least one fermionic generator. This gives "logarithmic" W-algebra extensions of a fractional-level ^sl(2) algebra. We discuss crucial aspects of the emerging…

A classical tool in the study of real closed fields are the fields $K((G))$ of generalised power series (i.e., formal sums with well-ordered support) with coefficients in a field $K$ of characteristic 0 and exponents in an ordered abelian…

Let R be a ring. Let SSE-R be the equivalence relation on square matrices (allowed to have different size) over R generated by A ~ B if there exist matrices U,V over R such that A = UV and B = VU . An invariant of SSE-R is shift equivalence…

Let S be a polynomial ring over a field of characteristic zero in finitely may variables. Let T be an unramified, finitely generated extension of S with $T^\times = k^\times$. Then T = S.

Let $ L((T^{-1}))$ be the space of (inverse) Laurent serieswith coefficients in some field $L$. It has a standard degree map and the induced topology. With its usual addition and a new product on this space which is continuous and preserves…

Suslin proved that for an extension K/k of algebraically closed fields the induced maps K_m(k)[n] --> K_m(K)[n] and K_m(k)/n ---> K_m(K)/n for the higher K-groups are isomorphisms, where A[n] is the subgroup of n-torsion in an abelien…

Given a field with a set of discrete valuations $V$, we show how the genus of a division algebra over the field is related to the genus of the residue algebras at various valuations in $V$ and the ramification data. When the division…