Formal groups arising from formal punctured ribbons

Derived Geometry and Non-Linear Differential Equations on the Punctured Disc

We study non-linear differential equations on the punctured formal disc by considering the natural derived enhancements of their spaces of solutions. In particular, by appealing to results of the inverse theory in the calculus of variations, we show that a variational formulation of a differential equation is \emph{equivalent} to the residue pairing inducing a (-1)-symplectic form on the derived space of solutions equipped with a certain decoration of its tangent complex.

Calculation of local formal Mellin transforms

Much recent work has been done on the local Fourier transforms for connections on the punctured formal disk. Specifically, the local Fourier transforms have been introduced, shown to induce certain equivalences of categories, and explicit formulas have been found to calculate them. In this paper, we prove analogous results in a similar situation, the local Mellin transforms for connections on the punctured formal disk. Specifically, we introduce the local Mellin transforms and show that they induce equivalences between certain categories of vector spaces with connection and vector spaces with …

Calculation of local formal Fourier transforms

We calculate the local Fourier transforms for connections on the formal punctured disk, corroborating the results of J. Fang and C. Sabbah using a different method. Our method is similar to Fang's, but more direct.

A Relative Lubin-Tate Theorem via Meromorphic Formal Geometry

We formulate a theory of punctured affine formal schemes, suitable for certain problems within algebraic topology. As an application, we show that the Morava K-theoretic localizations of Morava E-theory corepresent a version of the Lubin-Tate moduli problem in this framework.

伴随、环绕与无穷远处的态射

Adjoints, wrapping, and morphisms at infinity

本文证明光滑真范畴局部化中无穷远邻域的态射可由局部化函子左右伴随间的自然锥计算，从而统一恢复Ganatra–Gao–Venkatesh关于环绕Fukaya范畴的Rabinowitz环绕结果。

形式 torsor 的模空间

Moduli of formal torsors

本文构造了特征 p > 0 下形式穿孔圆盘上由 p-群与驯顺循环群半直积给出的有限群 torsor 的模叠，并证明其为具有有限万有单射转移映射的分离 Deligne-Mumford 叠的极限。

形式 Bott-Thurston 上循环与形式 Riemann-Roch 定理的一部分

Formal Bott-Thurston cocycle and part of a formal Riemann-Roch theorem

本文引入并研究形式 Bott-Thurston 上循环，证明其给出的中心扩张等价于行列式中心扩张的 12 重 Baer 和，并由此证明新的形式 Riemann-Roch 定理的一部分，应用于 $\mathbb Q$ 上分离概形的环化空间。