[過去ログ] Interーuniversal geometryとABC予想(応用スレ)51 (1002レス)
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576(1): 2021/02/15(月)23:09 ID:SCw6yhUQ(5/7) AAS
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(4)【ガロアの逆問題特論セミナー(I)】
June 5 (Mon) [理D505] 13:30-14:30+ (advanced talk 1)
Title: On the Malle conjecture and the self-twisted cover
Abstract: The Malle conjecture predicts that the number of Galois
extensions of Q with given group G and discriminant bounded by some
real number y > 0 grows like y^a, for some exponent a > 0. This
statement is known for nilpotent groups. The work I will present
establishes it for Sn, An, many simple groups and more generally all
regular Galois groups overQ. The constructed extensions can be further
requested to satisfy some notable local conditions. Our method uses a
new version of Hilbert's Irreducibility Theorem that counts
specialized extensions and not just the specialization points. A new
ingredient is the self-twisted cover that we will introduce.
(5)【ガロアの逆問題特論セミナー(II)】
June 6 (Tue) [理D505] 15:00-16:00+ (advanced talk 2)
Title: Genus zero pull-backs of Galois covers
Abstract: Pulling back a Galois cover $X\to \P^1$ of group $G$ along a
cover $\P^1\to \P^1$ yields ``most of the time'' a new Galois cover of
$\P^1$ with the same group. This operation provides a natural tool for
Inverse Galois Theory and induces a pre-order on the set of Galois
covers. We will present questions that arise from this double
perspective, and some answers.
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