Related papers: Trace formula for component groups of N\'eron mode…

Positive twisted traces are mathematical objects that could be useful in computing certain parameters of superconformal field theories. The case when $\mathcal{A}$ is a $q$-Weyl algebra and $\rho$ is a certain antilinear automorphism of…

We show how some of our recent results clarify the relationship between the L\^e numbers and the cohomology of the Milnor fiber of a non-isolated hypersurface singularity. The L\^e numbers are actually the ranks of the free Abelian groups…

It is found that the 2-index potential in nonabelian theories does not behave geometrically as a connection but that, considered as an element of the second de Rham cohomology group twisted by a flat connection, it fits well with all the…

We define a variant of normal basis, called a {\em Galois scaffolding}, that allows for an easy determination of valuation, and has implications for Galois module structure. We identify fully ramified, elementary abelian extensions of local…

Let A be an abelian variety over C such that the semisimple part of the Hodge group of A is a product of copies of SU(p,1) for some p>1. We show that any effective Tate twist of a Hodge structure occurring in the cohomology of A is…

We construct, out of modular symbols, 1-traces that are invariant with respect to the actions of the Hopf algebra $\Hc_{1}$ on the crossed product $\Ac_{Q}$ of the algebra of modular forms of all levels by $\GL^+ (2,Q)$ investigated in…

Motivated by the theory of bi-singular pseudodifferential operators, we introduce a two dimensional version of the Adler-Manin trace. Our construction is rather general in the sense that it involves a twist afforded by an algebra…

We study quadratic forms that can occur as trace forms of Galois field extensions L/K, under the assumption that K contains a primitive 4th root of unity. M. Epkenhans conjectured that any such form is a scaled Pfister form. We prove this…

The computation of the cohomology for finite groups of Lie type in the describing characteristic is a challenging and difficult problem. In earlier work, the authors constructed an induction functor which takes modules over the finite group…

We give a new sufficient condition for the normal extensions in an admissible Galois structure to be reflective. We then show that this condition is indeed fulfilled when X is the (protomodular) reflective subcategory of S-special objects…

We propose that there is a unique expansion for the string theory S-matrix elements of tachyons that corresponds to non-abelian tachyon action. For those S-matrix elements which, in their expansion, there are the Feynman amplitudes…

To every abelian subvariety of a principally polarized abelian variety $(A, \mathcal{L})$ we canonically associate a numerical class in the N\'eron-Severi group of $A$. We prove that these classes are characterized by their intersection…

If A is an Abelian variety, endowed with a polarization L, we study the function N_A(t) which counts the number of Abelian subvarieties S in A such that for the induced polarization L|_S the Euler characteristic \chi(L|_S) is bounded above…

We explicitly describe the Albanese morphism of a hyperelliptic variety, i.e., the quotient $X$ of an abelian variety $A$ by a finite group $G$ acting freely and not only by translations, by giving a description of the Albanese variety and…

In this manuscript, we consider non-abelian Anderson $A$-modules $E$ (of generic characteristic). The main results are on the structure of their motives, and on comparison isomorphisms between their cohomological realizations. In the center…

We consider compact homogeneous spaces G/H of positive Euler characteristic endowed with an invariant almost complex structure J and the canonical action \theta of the maximal torus T ^{k} on G/H. We obtain explicit formula for the…

We present a strategy to use the stable trace formula to compute growth in the cohomology of cocompact arithmetic lattices in a reductive group $G$. We then implement it in the case where $G = U(2,1)$, using results of Rogwaski. This…

In this article, we give a bound for the wild ramification of the monodromy action on the nearby cycles complex of a locally constant \'etale sheaf on the generic fiber of a smooth scheme over an equal characteristic trait in terms of Abbes…

We introduce the notion of cofoliation on a stack. A cofoliation is a change of the differentiable structure which amounts to giving a full representable smooth epimorphism. Cofoliations are uniquely determined by their associated Lie…

We calculate the formal group law which represents the completion of the N\'eron model of an algebraic torus over the rationals that splits in a tamely ramified abelian extension. As a tools in the proof, we define and give criterions to…