Related papers: Theta-functions for indefinite polarizations

Let $X$ be an irreducible singular Riemann surface, with desingularisation $\widetilde X$. The generalised Jacobian $J(X)$ of $X$ fibers over the Jacobian $J(\widetilde{X})$ of $\widetilde X$, and there is an Abel map $A$ of $\widetilde X$…

Following an idea of Totaro, we prove that the classical integral cycle class map from algebraic cycles to \'etale cohomology factors through a quotient of $\ell$-adic \'etale cobordism over an algebraically closed field of positive…

Inspired by the construction of Higher Hida theory of Boxer and Pilloni, we develop Higher Hida theory for the cohomology of the line bundles of Drinfeld modular forms on the Drinfeld modular curve. We also interpolate Serre duality.

We derive finite rational formulas for the traces of cycle integrals of certain meromorphic modular forms. Moreover, we prove the modularity of a completion of the generating function of such traces. The theoretical framework for these…

The cohomology theory known as Tmf, for "topological modular forms," is a universal object mapping out to elliptic cohomology theories, and its coefficient ring is closely connected to the classical ring of modular forms. We extend this to…

We prove a factorization theorem of generalized functions for moduli spaces of semistable parabolic bundles of any rank.

Let $A$ be a unital Banach algebra. We give a characterization of the left Banach $A$-modules $X$ for which there exists a commutative unital $C^*$-algebra $C(K)$, a linear isometry $i\colon X\to C(K)$, and a contractive unital homomorphism…

Let X be a smooth projective curve of genus at least two over the complex numbers. A pair (E,\phi) over X consists of an algebraic vector bundle E over X and a holomorphic section \phi of E. There is a concept of stability for pairs which…

In this note we introduce zeta functions and L-functions for discrete and faithful representations of surface groups in PSL(d, R), for d >= 3. These are natural generalizations of the wellknown classical Selberg zeta function and L-function…

We survey recent progress on the cohomology of moduli spaces of stable curves through the lens of the Hodge and Tate conjectures, especially their generalized coniveau forms, which relate Hodge structures and l-adic Galois representations…

We construct certain operations on stable moduli spaces and use them to compare cohomology of moduli spaces of closed manifolds with tangential structure. We obtain isomorphisms in a stable range provided the $p$-adic valuation of the Euler…

The quandle homology theory is generalized to the case when the coefficient groups admit the structure of Alexander quandles, by including an action of the infinite cyclic group in the boundary operator. Theories of Alexander extensions of…

The paper consists of two sections. The first section provides a new definition of mirror symmetry of abelian varieties making sense also over $p$-adic fields. The second section introduces and studies quantized theta-functions with…

I give a formula for the zeta function of a projective toric hypersurface over a finite field and estimate its Newton polygon. As an application this formula allows us to compute the exact number of rational points on the families of…

There is a huge amount of work on different kinds of theta functions, the theta correspondence, cohomology classes coming from special Schwartz classes via theta distribution, and much more. The aim of this text is to try to find joint…

We study the moduli space of meromorphic 1-forms on complex algebraic curves having at most simple poles with fixed nonzero residues. We interpret the Bergman tau function on this moduli space as a section of a line bundle and study its…

We introduce and study a family of power series, which we call Theta series, whose coefficients are in the tensor square of a quantum loop algebra. They arise from a coproduct factorization of the T-series of Frenkel--Hernandez, which are…

The simplicial wedge construction on simplicial complexes and simple polytopes has been used by a variety of authors to study toric and related spaces, including non-singular toric varieties, toric manifolds, intersections of quadrics and…

The local topological zeta function is a rational function associated to a germ of a complex holomorphic function. This function can be computed from an embedded resolution of singularities of the germ. For nondegenerate functions it is…

We prove that extension groups in strict polynomial functor categories compute the rational cohomology of classical algebraic groups. This result was previously known only for general linear groups. We give several applications to the study…