The étale theta function and its Frobenioid-theoretic manifestations

DOI10.2977/prims/1234361159zbMath1170.14023OpenAlexW1977006361WikidataQ47015402 ScholiaQ47015402MaRDI QIDQ1016588

Shinichi Mochizuki

Publication date: 6 May 2009

Published in: Publications of the Research Institute for Mathematical Sciences, Kyoto University (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2977/prims/1234361159

zbMATH Keywords

fundamental grouptheta functionsanabelian geometry

Mathematics Subject Classification ID

Coverings of curves, fundamental group (14H30) Theta functions and curves; Schottky problem (14H42)

Related Items (7)

Bogomolov's proof of the geometric version of the Szpiro conjecture from the point of view of inter-universal Teichmüller theory ⋮ Explicit estimates in inter-universal Teichmüller theory ⋮ Arithmetic deformation theory via arithmetic fundamental groups and non-Archimedean theta-functions, notes on the work of Shinichi Mochizuki ⋮ Inter-universal Teichmüller theory. I: Construction of Hodge theaters ⋮ Inter-universal Teichmüller theory. II: Hodge-Arakelov-theoretic evaluation ⋮ Inter-universal Teichmüller theory. III: Canonical splittings of the log-theta-lattice ⋮ Inter-universal Teichmüller theory. IV: Log-volume computations and set-theoretic foundations

Cites Work

• Absolute anabelian cuspidalization of proper hyperbolic curves
• On a geometric description of \(\text{Gal}(\bar{\mathbb Q}_p/\mathbb Q_p)\) and a \(p\)-adic avatar of \(\widehat{GT}\)
• The absolute anabelian geometry of canonical curves
• The geometry of anabelioids
• The local pro-p anabelian geometry of curves
• A combinatorial version of the Grothendieck conjecture
• Semi-graphs of anabelioids
• Galois Sections in Absolute Anabelian Geometry
• THE GEOMETRY OF FROBENIOIDS II: POLY-FROBENIOIDS
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