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My preprints or postprints:

1. Geometry of cohomology support loci for local systems I (published in J. Alg. Geom. 1997)
2. Geometry of cohomology support loci II: integrability of Hitchin's map (1997)
3. (with M. Nori) Solvable fundamental groups of algebraic varieties and Kaehler manifolds (published in Compositio Math. 1999)
4. Building mixed Hodge structures (in: The arithmetic and geometry of algebraic cycles, AMS 2000 )
5. (with P. Sastry) Intermediate Jacobians and Hodge Structures of Moduli Spaces (published in Proc. Ind. Acad. Sci. 2000)
6. A class of sheaves satisfying Kodaira's vanishing theorem (published in Math. Ann. 2000)
7. (with S. Archava) Kodaira dimension of symmetric powers ( published in Proc. AMS 2003)
8. Hodge cycles on some moduli spaces
9. (+ appendix by D. Keeler) Frobenius amplitude and strong vanishing theorems for vector bundles (published Duke Math. J, 2004)
10. The Leray spectral sequence is motivic (published in Inventiones Math. 2005)
11. Kahler Solvmanifolds (published Internat. Math. Res. Notices, 2004)
12. Partial regularity and amplitude (published in Amer. J. Math, 2006)
13. (with S-J. Kang) Functoriality of the coniveau filtration Canad. Math. Bull. (2007)
14. Motivation for Hodge cycles (published in Advances in Math, 2006)
15. The Hodge conjecture for rationally connected fivefolds
16. (with S-J. Kang) Coniveau and the Grothendieck group of varieties (published in Mich. Math. J., 2006)
17. (with A. Dhillon) The motive of the moduli stack of G-bundles over the universal curve ( Proc. Ind. Acad. Sci., 2008)
18. Mixed Hodge structures associated to geometric variations (in Cycles, Motives, Shimura Varieties, TIFR Mumbai)
19. Varieties with very little transcendental cohomology (published in Motives and Algebraic Cycles, Fields Inst. 2009)
20. An abelian category of motivic sheaves (Advances in Math 2013)
21. Frobenius Amplitude and Vanishing on Singular Spaces ( Illinois J. Math 2011)
22. (with M. Kumar) Beilinson-Hodge cycles on semiabelian varieties (Math. Res. Let., 2009)
23. The Hodge theoretic fundamental group and its cohomology (published in Geom. of Alg. Cycles, Clay Inst. 2010)
24. (with P. Baktary, J. Wlodarczyk) The combinatorial part of the cohomology of a singular variety.
25. Homomorphisms between Kaehler groups (published in topology of algebraic varieties and singularities, AMS 2011)
26. (with P. Baktary, J. Wlodarczyk) Weights on cohomology, invariants of singularities, and dual complexes (replaces earlier paper; published in Math. Ann.)
27. Hodge theory of cyclic covers branched over a union of hyperplanes (Can J. Math 2014)
28. (with X. Chen, S-J. Kang) The smooth center of the cohomology of a singular variety (published in Hodge theory, complex geometry, and representation theory, AMS 2014)
29. Decomposition of direct images of logarithmic differentials (Internat. Math. Res. Notices 2015)
30. Restrictions on the prime-to-p fundamental group of a smooth projective variety (published in Compositio 2015)
31. Geometric Hodge structures with prescribed Hodge numbers (Recent Advances in Hodge Theory, Cambridge)
32. (with P. Solapurkar) A new class of surfaces with maximal Picard number.
33. (with A. Dimca, R. Hain) On the fundamental groups of normal varieties ( Com. Contemp Math 2016)
34. Toward the structure of fibered fundamental groups of projective varieties. (Journ. de l'Ecole Polytech. 2017)
35. A Lefschetz (1,1) theorem for singular varieties.
36. Simpson's construction of varieties with many local systems. (Hodge theory and L² analysis)
37. Kodaira-Saito vanishing via Higgs bundles in positive characteristic. (Crelle's Journ. 2019)
38. (with J. Katz, D. B. McReynolds, P. Solapurkar) Integral Gassman equivalence of algebraic and hyperbolic manifolds (Math. Zeit. 2019)
39. Lefschetz decompositions for eigenforms on a Kahler manifold. (Proc. AMS 2018)
40. (with F. Hao, H. Li) Vanishing theorems for parabolic Higgs bundles (Math. Res. Let. 2019)
41. Algebraic cycles on genus two modular fourfolds. (Algebra & Numb. Theory 2019)
42. (with K. Matsuki, D. Patel, J. Wlodarczyk) A Kawamata-Viehweg type formulation of the Logarithmic Akizuki-Nakano Vanishing Theorem (Math. Zeit 2023)
43. Motivic sheaves revisited. (J. Pure & App. Algebra 2023)
44. When are braid groups of manifolds Kahler
45. Hodge cycles and the Leray filtration (Pacific J. Math 2022)
46. (with B. Wang) Perverse sheaves on varieties with large fundamental groups (to appear in J. Diff. Geom.)
47. Residues of connections and the Chevalley-Weil formula for curves (Enseignement Math 2022)
48. (with S. Hiatt) Equivariant Hodge modules and rational singularities (to appear in Michigan Math. J)
49. (with L. Maxim, B. Wang) Hodge-theoretic variants of the Hopf and Singer Conjectures (to appear Proc. of Conf. on Singer-Hopf)
50. (with D. Patel) Nonnegativity of signed Euler characteristics of moduli of curves and abelian varieties
51. (with S. Hiatt) Differential forms and Hodge structures on singular varieties

• Some applications of positive characteristic techniques to vanishing theorems (pdf file), Talk at Lipman Conf.
• Higgs Bundles, Integrability, and holomorphic forms (dvi file) (published in Motives, Polylogarithms and Hodge theory, Int'l Press 2002)
• Intro to mixed Hodge modules (pdf file) (published in Cycles, Motives and Shimura varieties, TIFR 2010)
• Cohomology support loci for local systems and Higgs bundles Talks at U. Michigan
• (with S.-J. Kang) Kahler-de Rham cohomology and Chern classes (Comm. Alg. 2011)

• Notes on Algebra
• Algebraic Geometry over the complex numbers (Springer)
• An introduction to differential forms (pdf file)
• Introduction to algebraic geometry (web page)
• A gallery of complex curves (web page)
• Introduction to etale cohomology
• Abelian varieties and moduli
• Homological algebra
• Purity for intersection cohomology after Deligne-Gabber

Other links:

• ArXiv
• The American Math Society
• Purdue math department home page
• MathSciNet
• Back issues of Publ. IHES (including EGA)

You can contact me via email at arapura*math.purdue.edu, where * should be replaced by @ , or you can contact me by phone at (765) 494-1983, or by mail at