Kummer Köprüsü: Bloch-Ogus Teorisi ile Regülatör Ayrışımı ve Semi-Order Law → Theorem 6.2 Birleşimi

We prove, via Bloch–Ogus theory, a block-diagonal decomposition of the p-adic syntomic regulator matrix for the Kummer surface X_t = Kum(E_t × E_t), where E_t is an elliptic family with a rank-1 jump at t_c. The decomposition turns the Semi-Order Law (|L(E_t,1)| ∼ C|t − t_c|^{1/2}) into a Theorem-6.2-type regulator singularity, det R_p(X_t) ∼ u·[log_p(t − t_c)]², thereby unifying the two earlier works through the Kummer construction. An expository appendix explains the proof strategy and states precisely why the remaining Conjecture 7.1 is not yet a theorem.

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-10-08
DOI
https://doi.org/10.5281/zenodo.23240216
Primary Topic
Algebraic Geometry and Number Theory
Type
preprint
Controls
|||
ALL TIME
JAN
FEB
MAR
APR
MAY
JUN
JUL
AUG
SEP
OCT
preprint

Kummer Köprüsü: Bloch-Ogus Teorisi ile Regülatör Ayrışımı ve Semi-Order Law → Theorem 6.2 Birleşimi

Eyüp CEBE
Zenodo (CERN European Organization for Nuclear Research)
Algebraic Geometry and Number Theory
preprint

Kummer Köprüsü: Bloch-Ogus Teorisi ile Regülatör Ayrışımı ve Semi-Order Law → Theorem 6.2 Birleşimi

Eyüp CEBE
preprint en

Abstract

We prove, via Bloch–Ogus theory, a block-diagonal decomposition of the p-adic syntomic regulator matrix for the Kummer surface X_t = Kum(E_t × E_t), where E_t is an elliptic family with a rank-1 jump at t_c. The decomposition turns the Semi-Order Law (|L(E_t,1)| ∼ C|t − t_c|^{1/2}) into a Theorem-6.2-type regulator singularity, det R_p(X_t) ∼ u·[log_p(t − t_c)]², thereby unifying the two earlier works through the Kummer construction. An expository appendix explains the proof strategy and states precisely why the remaining Conjecture 7.1 is not yet a theorem.

Zenodo (CERN European Organization for Nuclear Research)
Algebraic Geometry and Number Theory
AI Navigator

Ask Laika to Summarize, Analyze, and Connect papers live on the map.

Summarize Papers & Methodologies

Extract key findings, datasets, and comparative methods across publications.

Benchmark Rankings & Visual Analytics

Rank top research institutions, authors, funders, topics, and journals by Field-Weighted Citation Impact (FWCI) and paper volume with instant charts.

Connect Distant Disciplines

Bridge topological clusters on the map to find hidden collaborative intersections.

Kummer Köprüsü: Bloch-Ogus Teorisi ile Regülatör Ayrışımı ve Semi-Order Law → Theorem 6.2 Birleşimi — Eyüp CEBE · Zenodo (CERN European Organization for Nuclear Research) (2026) | TGRS Research Map | TGRS