Related papers: Varieties and pure symbols
Like categories, small 2-categories have well-understood classifying spaces. In this paper, we deal with homotopy types represented by 2-diagrams of 2-categories. Our results extend to homotopy colimits of 2-functors lower categorical…
This paper provides a full controlled version of algebraic $K$-theory. This includes a rich array of assembly maps; the controlled assembly isomorphism theorem identifying the controlled group with homology; and the stability theorem…
B. Totaro showed \cite{totaro} that the rational cohomology of configuration spaces of smooth complex projective varieties is isomorphic as an algebra to the $E_2$ term of the Leray spectral sequence corresponding to the open embedding of…
We recall some basic computations in the Milnor-Witt K-theory of a field, following Morel. We then focus on the Witt K-theory of a field of characteristic two and give an elementary proof of the fact that it is isomorphic as a graded ring…
We describe classes of toric varieties of codimension 2 which are either minimally defined by 3 binomial equations over any algebraically closed field, or are set-theoretic complete intersections in exactly one positive characteristic.
Up to a translation in the language of arithmetic $\D$-modules, we prove a conjecture of Berthelot on the preservation of the overconvergence under the direct image by a smooth proper morphism of varieties over a perfect field of…
Assume that R is a local regular ring containing an infinite perfect field, or that R is the local ring of a point on a smooth scheme over an infinite field. Let K be the field of fractions of R and the characteristic of K is not 2. Let X…
In the simple case of a Bernoulli shift on two symbols, zero and one, by permuting the symbols, it is obvious that any two equal entropy shifts are isomorphic. We show that the isomorphism can be realized by a factor that maps a binary…
The main results of this article concern the definition of a compactly supported cohomology class for the congruence group $\Gamma_0(p^n)$ with values in the second Milnor $K$-group (modulo 2-torsion) of the ring of $p$-integers of the…
For every algebraically closed field $\boldsymbol k$ of characteristic different from $2$, we prove the following: (1) Generic finite dimensional (not necessarily associative) $\boldsymbol k$-algebras of a fixed dimension, considered up to…
In this article we study the endomorphism algebras of abelian varieties $A$ defined over a given number field $K$ with large cyclic 2-torsion fields. A key step in doing so is to provide criteria for all the endomorphisms of $A$ to be…
This is the second of a series of two technical papers devoted to the analysis of holonomy invariants in strict higher gauge theory with end applications in higher Chern--Simons theory. We provide a definition of trace over a crossed module…
We determine the endomorphism categories of cell 2-representations of fiat 2-categories associated with strongly regular two-sided cells under some natural assumptions. Along the way, we completely describe J-simple fiat 2-categories which…
We extend the 2-representation theory of finitary 2-categories to certain 2-categories with infinitely many objects, denoted locally finitary 2-categories, and extend the classical classification results of simple transitive…
Euler-symmetric projective varieties are nondegenerate projective varieties admitting many C*-actions of Euler type. They are quasi-homogeneous and uniquely determined by their fundamental forms at a general point. We show that…
We characterize the smooth toric varieties for which the Merkurjev spectral sequence, connecting equivariant and ordinary K-theory, degenerates. We find under which conditions on the support of the fan the $E^2$ terms of the spectral…
We construct classes in the motivic cohomology of certain 1-parameter families of Calabi-Yau hypersurfaces in toric Fano n-folds, with applications to local mirror symmetry (growth of genus 0 instanton numbers) and inhomogeneous…
We present an algorithm solving the following problem: given two genus 2 curves over a field k with isogenous Jacobians, compute such an isogeny explicitly. This isogeny can be either an l-isogeny or, in the real multiplication case, an…
We study the behaviour of ordinary parts of the homology modules of modular curves, associated to a decreasing sequence of congruence subgroups ${\Gamma}_1(N2^r)$ for $r \geq 2$, and prove a control theorem for these homology modules.
Let K be a complete discretely valued field with residue field k. If char(K) = 0, char(k) = 2 and the 2-rank of k is d, we prove that there exists an integer N depending on d such that the u-invariant of any function field in one variable…