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, The status of the Scholze-Stix Report and an analysis of the Mochizuki-Scholze-Stix Controversy (pdf)

• Kirti Joshi, Final report on the Mochizuki-Scholze-Stix Controversy (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, Algebraization of Mochizuki’s anabelian variation of ring structures, perfectoid geometry and formal groups (arxiv:1906.06840)

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

• Kirti Joshi, The Absolute Grothendieck Conjecture is false for Fargues-Fontaine Curves (arxiv:2008.01228)

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

• Kirti Joshi, Christian Pauly, Opers of higher types, Quot-schemes and Frobenius instability loci (Épijournal de Géométrie Algébrique, Volume 4, 2020, Article Nr. 17)

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

• Kirti Joshi, Christian Pauly, Hitchin-Mochizuki morphism, opers and Frobenius-destabilized vector bundles over curves (Advances in Mathematics, Volume 274, Issue 9, April 2015, Pages 39–75)

On Frobenius destablized vector bundles on curves:

• Kirti Joshi, S. Ramanan, Jiu-Kang Yu and Eugene Z. Xia, On vector bundles destabilized by Frobenius pull-back (Compositio Mathematica, 142, Issue 3, 2006, Pages 616–630)

• Kirti Joshi, Eugene Z. Xia, Moduli of Vector Bundles on Curves in Positive Characteristics (Compositio Mathematica, Volume 122, Issue 3, 2000, Pages 315–321)

On Frobenius Splitting and Ordinarity:

• Kirti Joshi, C. S. Rajan, Frobenius Splitting and Ordinarity (International Mathematics Research Notices, Volume 2003, Issue 2, 2003, Pages 109–121)

On the Noether-Lefschetz Theorem:

• Kirti Joshi, A General Noether-Lefshetz Theorem and Applications (Journal of Algebraic Geometry, Vol. 4, Issue 1, 1995, Pages 105–135)

On the geography of low dimensional varieties in positive characteristics:

• Kirti Joshi, Crystalline aspects of geography of low dimensional varieties I: numerology (European Journal of Mathematics, Vol. 6, 2020, Pages 1111-1175)

Related entries

• Inter-universal Teichmüller theory

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