Manish Kumar
Statistics and Mathematics Unit,
Indian Statistical Institute, Bangalore Center
Office: S2
8th Mile Mysore Road
RVCE Post, Jnana Bharti
Bangalore - 560059, India
Email: manish at isibang dot ac dot in
Phone: +91-80-26985442; +91(0)80-2848 3002 (Extn 442)


Research interests

Algebraic Geometry, Commutative algebra, Arithmetic Algebraic Geometry.

Teaching

Seminars

Publications

On the stability of pulled back parabolic vector bundles (with Indranil Biswas and A. J. Parameswaran) to appear in Journal of Mathematical Sciences, University of Tokyo. arxiv page

Genuinely ramified maps and stability of pulled-back parabolic bundles (with Indranil Biswas and A. J. Parameswaran) to appear in Indagationes Mathematicae arxiv page

Higher dimensional formal orbifolds and orbifold bundles in positive characteristic (with Indranil Biswas and A. J. Parameswaran) Comm. Algebra 50 (2022), no. 1, 300–307. arxiv page

On Inertia Conjecture for Alternating group Covers (with Soumyadip Das) J. Pure Appl. Algebra 224 (2020), no. 9, 106363, 14 pp. arxiv page

Ramification theory and formal orbifolds in arbitrary dimension. Proc. Indian Acad. Sci. Math. Sci. 129 (2019), no. 3, Art. 38, 34 pp. pdf-file

Parabolic bundles in positive characteristic. (with Souradeep Majumder) J. Ramanujan Math. Soc. 33 (2018), no. 1, 1-36. pdf-file

Formal orbifolds and orbifold bundles in positive characteristic. (with A. J. Parameswaran) Internat. J. Math. 30 (2019), no. 12, 1950067, 20 pp. arxiv page

Embedding problems for open subgroups of the fundamental group. Ann. Inst. Fourier (Grenoble) 67 (2017), no. 6, 2623-2649. pdf-file

Compositum of wildly ramified extensions. J. Pure Appl. Algebra 218 (2014), no. 8, 1528-1536. pdf-file

Killing wild ramification. Israel J. Math. 199 (2014), no. 1, 421-431. pdf-file

Subgroup structure of fundamental groups in positive characteristic. (with Lior Bary-Soroker) Comm. Algebra, 41 (10), (2013). pdf-file

Fundamental group of affine curves in positive characteristic. J. Algebra 399 (2014), 323-342. pdf-file

Beilinson-Hodge cycles on semiabelian varieties. (with Donu Arapura) Math. Res. Lett. 16 (2009), no. 4, 557--562. pdf-file

Fundamental group in positive characteristic. J. Algebra 319 (2008), no. 12, 5178--5207. pdf

Simultaneous Surface Resolution in Quadratic and Biquadratic Galois Extensions. (with S.S. Abhyankar) Contemporary Mathematics, 390, Dec (2003), 1-8. pdf

Valuations and Rank of Ordered Abelian Groups. Proc. Amer. Math. Soc. 133 (2005), 343-348. pdf


Preprints

Pushforward of structure sheaf and virtual global generation. (with Indranil Biswas and A. J. Parameswaran) preprint available on request.

The tame Nori fundamental group. (with Indranil Biswas and A. J. Parameswaran) preprint available on request.

A criterion for solving embedding problems for the etale fundamental group of curves (with Poulami Mandal) preprint available on request.

Bertini type results and their applications. (with Indranil Biswas and A. J. Parameswaran) preprint available on request.

Galois closure of henselization. arxiv page

Cyclicity of certain division algebras over $k(\CC\PP^2)$ (with Rajesh Kulkarni) preprint available on request.

Beilinson-Tate cycles on semi-abelian varieties. (with Donu Arapura) preprint available on request.


Links
Mathscinet
Arxiv
MathOverflow
Conferences and Workshops
Essen SFB/TR 45
MSU math
Purdue Math