相关论文: Gau{\ss}-Manin determinant connections and periods…

see the old abstract and the comments here.

We give an explicit formula for the determinant of the Gau{\ss}-Manin connection for an irregular connection on a Zariski open set of the projective line $\P^1_K$ over a function field $K$ over a field $k$ of characteristic zero.

This is the last version of AG/0111277. Here the old abstract: We define $\epsilon$-factors in the de Rham setting and calculate the determinant of the Gau\ss-Manin connection for a family of (affine) curves and a vector bundle equipped…

Time-dependent structures often appear in differential geometry, particularly in the study of non-autonomous differential equations on manifolds. One may study the geodesics associated with a time-dependent Riemannian metric by extremizing…

In this article, we calculate the period determinant of an irrgular singular connection d+dy on the legendre curve U: y^2 =x(x-1)(x- lambda). We calculate its de Rham cohomology and the cycles in the homology of the dual connection and…

We consider the 2-cocycle deformation of algebras graded by discrete groups. The action of the Maurer-Cartan form on cyclic cohomology is shown to be cohomologous to the cup product action of the group cocycle. This allows us to compute the…

We use Getzler's Gauss-Manin connection to prove the invariance of periodic cyclic cohomology for the smooth deformation of noncommutative tori. We explicitly calculate the parallel translation maps and use them to describe the behavior of…

After an overview of noncommutative differential calculus, we construct parts of it explicitly and explain why this construction agrees with a fuller version obtained from the theory of operads.

In this note a generalized Gauss-Manin connection is constructed for cohomology of Lie-Rinehart algebras, generalizing the classical Gauss-Manin connection. As an application a Gysin-map between K-groups of flat connections is constructed.…

Given a smooth one parameter deformation of associative topological algebras, we define Getzler's Gauss-Manin connection on both the periodic cyclic homology and cohomology of the corresponding smooth field of algebras and investigate some…

We construct a canonical element, called the refined analytic torsion, of the determinant line of the cohomology of a closed oriented odd-dimensional manifold M with coefficients in a flat complex vector bundle E. We compute the Ray-Singer…

This paper aims to study the Betti homology and de Rham cohomology of twisted symmetric powers of the Kloosterman connection of rank two on the torus. We compute the period pairing and, with respect to certain bases, interpret these…

We show that the de Rham cohomology of any separated and smooth rigid variety over a field of Laurent series of characteristic zero carries a natural formal meromorphic connection, which we call the Gauss-Manin connection. We compare it…

We derive explicit formulas for some Kloosterman sums on $\Gamma_0(N)$, and for the Fourier coefficients of Eisenstein series attached to arbitrary cusps, around a general Atkin-Lehner cusp.

We study the Gauss-Manin connection for the moduli space of an arrangement of complex hyperplanes in the cohomology of a nonresonant complex rank one local system. Aomoto and Kita determined this Gauss-Manin connection for arrangements in…

We study differential forms on the universal vector extension $A^\natural$ of an abelian scheme $A$ in characteristic zero, and derive a new construction of the $D$-group scheme structure on $A^\natural$. This gives, in particular, a rather…

We study the branch divisors on the boundary of the canonical toroidal compactification of ball quotients. We show a criterion, the low slope cusp form trick, for proving that ball quotients are of general type. Moreover, we classify when…

To classify one-dimensional disordered quantum systems with chiral symmetry, we analyse the winding number of the determinant of a parametrized non-Hermitian random matrix field over the unit circle modelling the off-diagonal block of a…

Let $X/S$ be a smooth family of smooth projective varieties, where $S$ is a smooth affine curve over a field $k$ of characteristic $0.$ We relate the differential fundamental groupoid scheme of $X/k$ with the differential fundamental…

We use derived methods to study the Gauss-Manin connection in Hochschild homology, infinitesimal cohomology, and derived de Rham cohomology. As applications, we give new approaches to nilinvariance, the Quillen spectral sequence, and the…