Related papers: Refined height pairing
We define a notion of height for rational points with respect to a vector bundle on a proper algebraic stack with finite diagonal over a global field, which generalizes the usual notion for rational points on projective varieties. We…
Aperiodic point sets (or tilings) which can be obtained by the method of cut and projection from higher dimensional periodic sets play an important role for the description of quasicrystals. Their topological invariants can be computed…
We describe a differential graded Lie algebra controlling infinitesimal deformations of triples $(X,\mathcal{F},\sigma)$, where $\mathcal{F}$ is a coherent sheaf on a smooth variety $X$ over a field of characteristic 0 and $\sigma\in…
As an attempt to understand motives over $k[x]/(x^m)$, we define the cubical additive higher Chow groups with modulus for all dimensions extending the works of S. Bloch, H. Esnault and K. R\"ulling on 0-dimensional cycles. We give an…
We develop a machinery of Chen iterated integrals for higher Hochschild complexes. These are complexes whose differentials are modeled on an arbitrary simplicial set much in the same way the ordinary Hochschild differential is modeled on…
Let $f(\bfz,\bar\bfz)$ be a mixed strongly polar homogeneous polynomial of $3$ variables $\bfz=(z_1,z_2, z_3)$. It defines a Riemann surface $V:=\{[\bfz]\in \BP^{2}\,|\,f(\bfz,\bar\bfz)=0 \}$ in the complex projective space $\BP^{2}$. We…
When studying deformations of an $A$-module $M$, Laudal and Yau showed that one can consider 1-cocycles in the Hochschild cohomology of $A$ with coefficients in the bi-module $End_k(M).$ With this in mind, the use of higher order Hochschild…
Let R be a complete discrete valuation ring with algebraically closed residue field k and fraction field K. Let X_K be a projective smooth and geometrically connected scheme over K. N\'eron defined a canonical pairing on X_K between…
In this paper we construct a tilting sheaf for Severi-Brauer Varieties and Involution Varieties. This sheaf relates the derived category of each variety to the derived category of modules over a ring whose semisimple component consists of…
The height of a toric variety and that of its hypersurfaces can be expressed in convex-analytic terms as an adelic sum of mixed integrals of their roof functions and duals of their Ronkin functions. Here we extend these results to the…
We consider a Cartier divisor L on a d-dimensional complex projective variety X. It is well-known that the dimensions of the cohomomology groups H^i(X,O_X(mL)) grow at most like m^d, and it is natural to ask when one of these actually has…
If $X$ is a projective, geometrically irreducible variety defined over a finite field $\F_q$, such that it is smooth and its Chow group of 0-cycles fulfills base change, i.e. $CH_0(X\times_{\F_q}\bar{\F_q(X)})=\Q$, then the second author's…
Chevalley's theorem states that every smooth connected algebraic group over a perfect field is an extension of an abelian variety by a smooth connected affine group. That fails when the base field is not perfect. We define a pseudo-abelian…
We introduce a 1-cocycle on the group of diffeomorphisms Diff$(M)$ of a smooth manifold $M$ endowed with a projective connection. This cocycle represents a nontrivial cohomology class of $\Diff(M)$ related to the Diff$(M)$-modules of second…
Given a semisimple element in the loop Lie algebra of a reductive group, we construct a quasi-coherent sheaf on a partial resolution of the trigonometric commuting variety of the Langlands dual group. The construction uses affine Springer…
We construct new indecomposable elements in the higher Chow group CH2(A,1) of a principally polarized Abelian surface over a non Archimedean local field, which generalize an element constructed by Collino. These elements are constructed…
We introduce an affine Schur algebra via the affine Hecke algebra associated to Weyl group of affine type C. We establish multiplication formulas on the affine Hecke algebra and affine Schur algebra. Then we construct monomial bases and…
A central problem of algebraic topology is to understand the homotopy groups $\pi_d(X)$ of a topological space $X$. For the computational version of the problem, it is well known that there is no algorithm to decide whether the fundamental…
We consider a combinatorial reconfiguration problem on a subclass of quadrangulations of surfaces called square-tiled surfaces. Our elementary move is a shear in a cylinder that corresponds to a well-chosen sequence of diagonal flips that…
The paper was motivated by a question of Vilonen, and the main results have been used by Mirkovic and Vilonen to give a geometric interpretation of the dual group (as a Chevalley group over Z) of a reductive group. We define a…