arXiv subjects

Eita Haibara

Publications and source records attributed to Eita Haibara.

4 recordsLinked to original sources

arXiv2025

Derived analytic geometry: Derived Kähler space and Hodge theory

We introduce higher analytic geometry, a novel framework extending Lurie's derived complex analytic spaces. This theory generalizes classical complex analytic geometry, enabling the study of derived Kähler spaces with non-trivial higher homotopy groups. We develop derived de Rham and Dolbeault cohomologies, yielding a Hodge decomposition for compact derived Kähler spaces, and establish a derived Stokes' theorem, unifying classical results with homotopical structures.

math.AG↗

arXiv2025

Some memos on Stable Symplectic Structured Space

In these memos, we define a pregeometry $\mathcal{T}_{\mathbb{S}} ^{alg}$ and a geometry $\mathcal{G}_{\mathbb{S}} ^{alg}$ which integrate symplectic manifolds with $E_{\infty}$-ring sheaves, enabling the construction of $\mathcal{G}_{\mathbb{S}} ^{alg}$-schemes as structured $\infty$-topoi. Our framework and results establish a profound connection between algebraic invariants and homological properties, opening new pathways for exploring symplectic phenomena through the lens of higher category theory and derived geometry.

math.AG↗

arXiv2025

Some memos on Stable Symplectic Structured Space II: Symplectic motives

These memos include the research on $\mathcal{G}_{\mathbb{S}}^{alg}$-scheme theory, the definition of symplectic motives over $\mathcal{G}_{\mathbb{S}}^{alg}$-schemes and symplectic motivic cohomology. This presents a new research direction.

math.AG↗

arXiv2024

Relative-Hyper GAGA Theorem

In this paper, we provide a relative hypercohomology version of Serre's GAGA theorem. We prove that the relative hypercohomology of a complex of sheaves on a complex projective variety is isomorphic to the relative hypercohomology of its analytification, with respect to an open or closed subvariety. This result implies Serre's original GAGA theorem.

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