Integral Local Invariant Cycles in Degree One

For a semistable one-parameter family of complex projective varieties with smooth nearby fiber $X_t$ and monodromy $T$, is the map $H^1(X, \mathbb{Z}) \to H^1(X_t, \mathbb{Z})^T$ surjective? True in degree one, although the integral statement fails in higher degree.

Result

Proved

Status

Resolved

AI contribution

AI-discovered

Method

Argument

Field

Algebraic geometry

Posed by

—

Year posed

2026

Years open

0y

Solved

2026-05-17

Model

QED (GPT-5.5)

Vendor

OpenAI

Collaborators

—

Verification

Independently expert-verified

Publication

Preprint

Significance

5 / 100*

Disclosed cost

—

Wikipedia

No dedicated article