Tootfinder

Locally analytic completed cohomology of Shimura varieties of Hodge type
Kensuke Aoki
https://arxiv.org/abs/2508.11099 https://arxiv.org/pdf/2508.11099

Locally analytic completed cohomology of Shimura varieties of Hodge type
For Shimura varieties of Hodge type, we show that there are natural isomorphisms between locally analytic complete cohomology groups and cohomology groups for flag varieties with coefficient which is given by their perfectoid covers. This result is a generalization of that of Pan for the modular curve and Qiu-Su for unitary Shimura curves.

Replaced article(s) found for math-ph. https://arxiv.org/list/math-ph/new
[1/1]:
- A generalization of the Witten conjecture through spectral curve
Shuai Guo, Ce Ji, Qingsheng Zhang

Topological Jacobi Forms
Tilman Bauer, Lennart Meier
https://arxiv.org/abs/2508.08010 https://arxiv.org/pdf/2508.08010

Topological Jacobi Forms
As a generalization of the ring spectrum of topological modular forms, we construct a graded ring spectrum of topological Jacobi forms, $\operatorname{TJF}_*$. This is constructed as the global sections of a sheaf of $E_\infty$-ring spectra on the stacky universal elliptic curve using circle-equivariant $\operatorname{TMF}$. Complete calculations of its homotopy at odd primes and partial results at $p=2$ are given.

Phase field approximation for Plateau's problem: a curve geodesic distance penalty approach
Matthieu Bonnivard, Elie Bretin, Antoine Lemenant, Eve Machefert
https://arxiv.org/abs/2506.22273

Phase field approximation for Plateau's problem: a curve geodesic distance penalty approach
This work focuses on a phase field approximation of Plateau's problem. Inspired by Reifenberg's point of view, we introduce a model that combines the Ambrosio-Torterelli energy with a geodesic distance term, which can be considered as a generalization of the approach developed by Bonnivard, Lemenant and Santambrogio to approximate solutions to Steiner's problem. First, we present a Gamma-convergence analysis of this model in the simple case of a single curve located on the edge of a cylinder. I…

This https://arxiv.org/abs/2103.01285 has been replaced.
link: https://scholar.google.com/scholar?q=a

On the intersection cohomology of the moduli of $\mathrm{SL}_n$-Higgs bundles on a curve
We explore the cohomological structure for the (possibly singular) moduli of $\mathrm{SL}_n$-Higgs bundles for arbitrary degree on a genus g curve with respect to an effective divisor of degree >2g-2. We prove a support theorem for the $\mathrm{SL}_n$-Hitchin fibration extending de Cataldo's support theorem in the nonsingular case, and a version of the Hausel-Thaddeus topological mirror symmetry conjecture for intersection cohomology. This implies a generalization of the Harder-Narasimhan theor…

A Topological Perspective on the Birch and Swinnerton Dyer Conjectures
Maisara Shoeib
https://arxiv.org/abs/2505.19796 https://arxiv.…

A Topological Perspective on the Birch and Swinnerton Dyer Conjectures
This paper presents a topological framework for investigating the Birch and Swinnerton Dyer conjecture through four dimensional embeddings of elliptic curves. We propose a correspondence between the algebraic rank of an elliptic curve and the number of topologically independent loops in its embedding, which appears to be related to the order of vanishing of its L function at s=1. Our computational function F new and its generalization F_(m,s) provide methods for examining this relationship thro…