nLab Kirti Joshi

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Selected writings

On p-adic Teichmüller theory:

• Kirti Joshi, Construction of Arithmetic Teichmüller Spaces and some applications (arXiv:2106.11452)

• Kirti Joshi, Untilts of fundamental groups: construction of labeled isomorphs of fundamental groups – Arithmetic Holomorphic Structures (arXiv:2210.11635)

• Kirti Joshi, Construction of Arithmetic Teichmüller spaces II: Proof of a local prototype of Mochizuki’s Corollary 3.12 (arXiv:2303.01662)

• Kirti Joshi, Construction of Arithmetic Teichmüller spaces II($\frac{1}{2}$): Deformations of Number Fields (arXiv:2305.10398)

• Kirti Joshi, Comments on Arithmetic Teichmüller Spaces (arXiv:2111.06771)

• Kirti Joshi, Mochizuki’s Corollary 3.12 and my quest for its proof [pdf]

• Kirti Joshi, (Older-Version) Construction of Arithmetic Teichmuller spaces II: Towards Diophantine Estimates (arXiv:2111.04890)

• Kirti Joshi, (Older-Version) Untilts of fundamental groups: construction of labeled isomorphs of fundamental groups (arXiv:2010.05748)

Claim of proof of statements similar to Mochizuki's corollary 3.12:

• Kirti Joshi, Appendix to Construction of Arithmetic Teichmüller spaces II($\frac{1}{2}$): Deformations of Number Fields (arXiv:2305.10398)

• Kirti Joshi, Construction of Arithmetic Teichmuller Spaces III: A Rosetta Stone and a proof of Mochizuki’s Corollary 3.12 (arXiv:2401.13508)

Claim of proof of the abc conjecture:

• Kirti Joshi, Construction of Arithmetic Teichmuller Spaces IV: Proof of the abc-conjecture (arXiv:2403.10430)

On anabelian geometry:

• Kirti Joshi, Mochizuki’s anabelian variation of ring structures and formal groups (arxiv:1906.06840)

• Kirti Joshi, On Mochizuki’s idea of Anabelomorphy and its applications (arxiv:2003.01890)

On the Hitchin-Mochizuki morphism and Frobenius destablized vector bundles on curves:

• Kirti Joshi, Christian Pauly, Hitchin–Mochizuki morphism, opers and Frobenius-destabilized vector bundles over curves ([Advances in Mathematics,]

  Volume 274, 9 April 2015, Pages 39-75] (https://doi.org/10.1016/j.aim.2015.01.004))

• Kirti Joshi, The Degree of the Dormant Operatic Locus (International Mathematics Research Notices, Volume 2017, Issue 9, May 2017, Pages 2599–2613)

Related entries

• Inter-universal Teichmüller theory

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