Related papers: The Abelian-Nonabelian Correspondence for $I$-func…

We give an explicit approach to quotienting affine varieties by linear actions of linear algebraic groups with graded unipotent radical, using results from projective Non-Reductive GIT. Our quotients come with explicit projective…

For an Abelian surface $A$ with a symplectic action by a finite group $G$, one can define the partition function for $G$-invariant Hilbert schemes \[Z_{A, G}(q) = \sum_{d=0}^{\infty} e(\text{Hilb}^{d}(A)^{G})q^{d}.\] We prove the reciprocal…

We prove the existence of a module for the largest Mathieu group, whose trace functions are weight two quasimodular forms. Restricting to the subgroup fixing a point, we see that the integrality of these functions is equivalent to certain…

Let $(Z,\omega)$ be a \Keler manifold and let $U$ be a compact connected Lie group with Lie algebra $\mathfrak{u}$ acting on $Z$ and preserving $\omega$. We assume that the $U$-action extends holomorphically to an action of the complexified…

In this paper, we partially extend recent results of Wan concerning the relationship between the zeta functions of a Calabi-Yau hypersurface and its (singular) mirror variety.

We describe a generalization of Gabriel and Zisman's Calculus of Fractions to quasicategories, showing that the two essentially coincide for the nerve of a category. We then prove that the marked Ex-functor can be used to compute the…

We give an algebraic analog of the functional equation of Riemann's theta function. More precisely, we define a `theta multiplier' line bundle over the moduli stack of principally polarized abelian schemes with theta characteristic and…

Let $G$ be an affine algebraic group over an algebraically closed field $k$ of characteristic zero. In this paper, we consider finite $G$-equivariant morphisms $F:X\to Y$ of irreducible affine $G$-varieties. First we determine under which…

Recently Alday, Gaiotto and Tachikawa proposed a conjecture relating 4-dimensional super-symmetric gauge theory for a gauge group G with certain 2-dimensional conformal field theory. This conjecture implies the existence of certain…

We prove that an abelian category equipped with an ample sequence of objects is equivalent to the quotient of the category of coherent modules over the corresponding algebra by the subcategory of finite-dimensional modules. In the…

We prove a formula of the equivariant infinity-adic special L-values of abelian t-modules. This gives function field analogues of the equivariant class number formula. As an application, we calculate the special values of Artin L-functions…

We will prove that, for any abelian group $G$, the canonical (surjective and continuous) mapping $\boldsymbol{\beta}G \to {\frak b}G$ from the Stone-\v{C}ech compactification $\boldsymbol{\beta}G$ of $G$ to its Bohr compactfication ${\frak…

We prove that for every reductive group G with a maximal torus T and the Weyl group W there is a natural normalization map chi from T^N/W to an irreducible component of the G-character variety of Z^N. We prove that chi is an isomorphism for…

Let $Y\mathord{/\mkern-6mu/}_\theta G$ be a complete intersection in a GIT quotient $X\mathord{/\mkern-6mu/}_\theta G$ cut out by a $G$-representation $E$. We show that the $E$-twisted quasimap $I$-function recovers invariants of $(Y, G,…

If f is a nonzero complex-valued function defined on a finite abelian group A and \hat f is its Fourier transform, then |Supp (f)||Supp {\hat f)| \ge |A|, where Supp (f) and Supp (\hat f) are the supports of f and \hat f. In this paper we…

For a globally generic cuspidal automorphic representation $\mathit{\Pi}$ of a quasi-split reductive group $G$ over $\mathbb Q$, E. Lapid and Z. Mao proposed a conjecture on the decomposition of the global Whittaker functionals on…

Let $G$ be a compact, connected Lie group and $T \subset G$ a maximal torus. Let $(M,\omega)$ be a monotone closed symplectic manifold equipped with a Hamiltonian action of $G$. We construct a module action of the affine nil-Hecke algebra…

For an irreducible subvariety Z in an algebraic group G we define a nonnegative integer gdeg(Z) as the degree, in a certain sense, of the Gauss map of Z. It can be regarded as a substitution for the intersection index of the conormal bundle…

We explore the notion of representation of an affine extension of an abelian variety -- such an extension is a faithfully flat affine morphism of $\Bbbk$-group schemes $q:G\to A$, where $A$ is an abelian variety. We characterize the…

We construct the Cartier duality equivalence for affine commutative group schemes $G$ whose coordinate ring is a flat Mittag-Leffler module over an arbitrary base ring $R$. The dual $G^\vee$ of $G$ turns out to be an ind-finite ind-scheme…