STNB2025 (38th edition)
Semistable abelian varieties over $\mathbb{Q}$ which have good reduction outside of $29$
Ponentes
Pip Goodman
Resumen
In joint work Francesco Campagna, we classify all such abelian varieties. The main difficulty in doing so is due to the existence of a simple group scheme $V$ of order $4$ which is everywhere locally reducible (but globally irreducible). This makes it hard to classify extensions of $V$ by itself. A key step in being able to do so comes from proving the failure of a type of local--global principle for finite flat group schemes.
In this talk I will give an introduction to finite flat group schemes and outline a proof of the above.
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