Abstract
Fresán, Sabbah, and Yu constructed motives
Acknowledgements
This work is based on the author’s Ph.D. thesis completed at Centre de Mathématiques Laurent Schwartz in École Polytechnique. The author thanks his supervisors, Javier Fresán and Claude Sabbah, for proposing this question to him and for their guidance and fruitful discussions. The author also thanks Alberto Castaño Domínguez, Lei Fu, and Christian Sevenheck for their feedback on a previous version of this article and to Gabriel Ribeiro, Bin Wang, Jeng-Daw Yu, and Bingyu Zhang for valuable discussions. Lastly, the author appreciates an anonymous referee for numerous suggestions to correct inaccuracies and enhance this paper’s presentation.
References
[1] A. Adolphson and S. Sperber, On twisted de Rham cohomology, Nagoya Math. J. 146 (1997), 55–81. 10.1017/S0027763000006218Suche in Google Scholar
[2] G. W. Anderson, Cyclotomy and an extension of the Taniyama group, Compos. Math. 57 (1986), no. 2, 153–217. Suche in Google Scholar
[3] D. Broadhurst, Feynman integrals, L-series and Kloosterman moments, Commun. Number Theory Phys. 10 (2016), no. 3, 527–569. 10.4310/CNTP.2016.v10.n3.a3Suche in Google Scholar
[4] D. Broadhurst, Critical L-values for products of up to 20 Bessel functions, Lecture slides (2017), https://www.matrix-inst.org.au/wp_Matrix2016/wp-content/uploads/2016/04/Broadhurst-2.pdf. Suche in Google Scholar
[5] P. Deligne, Cohomologie étale, Lecture Notes in Math. 569, Springer, Berlin 1977. 10.1007/BFb0091516Suche in Google Scholar
[6] P. Deligne, Théorie de Hodge irrégulière (mars 1984 & août 2006), Singularités irrégulières, Doc. Math. (Paris) 5, Société Mathématique de France, Paris (2007), 109–114, 115–128. Suche in Google Scholar
[7]
H. Esnault, C. Sabbah and J.-D. Yu,
[8] E. Frenkel and B. Gross, A rigid irregular connection on the projective line, Ann. of Math. (2) 170 (2009), no. 3, 1469–1512. 10.4007/annals.2009.170.1469Suche in Google Scholar
[9] J. Fresán and P. Jossen, Exponential motives, http://javier.fresan.perso.math.cnrs.fr/expmot.pdf,␣in␣preparation. Suche in Google Scholar
[10] J. Fresán, C. Sabbah and J.-D. Yu, Hodge theory of Kloosterman connections, Duke Math. J. 171 (2022), no. 8, 1649–1747. 10.1215/00127094-2021-0036Suche in Google Scholar
[11] J. Fresán, C. Sabbah and J.-D. Yu, Quadratic relations between periods of connections, Tohoku Math. J. (2) 75 (2023), no. 2, 175–213. 10.2748/tmj.20211209Suche in Google Scholar
[12] L. Fu and D. Wan, L-functions for symmetric products of Kloosterman sums, J. reine angew. Math. 589 (2005), 79–103. 10.1515/crll.2005.2005.589.79Suche in Google Scholar
[13] L. Fu and D. Wan, Trivial factors for L-functions of symmetric products of Kloosterman sheaves, Finite Fields Appl. 14 (2008), no. 2, 549–570. 10.1016/j.ffa.2007.07.005Suche in Google Scholar
[14] W. Fulton, Introduction to toric varieties, Ann. of Math. Stud. 131, Princeton University, Princeton 1993. 10.1515/9781400882526Suche in Google Scholar
[15] W. Fulton and J. Harris, Representation theory, Grad. Texts in Math. 129, Springer, New York 1991. Suche in Google Scholar
[16] J. Heinloth, B.-C. Ngô and Z. Yun, Kloosterman sheaves for reductive groups, Ann. of Math. (2) 177 (2013), no. 1, 241–310. 10.4007/annals.2013.177.1.5Suche in Google Scholar
[17] R. Hotta, K. Takeuchi and T. Tanisaki, D-modules, perverse sheaves, and representation theory, Progr. Math. 236, Birkhäuser, Boston 2008. 10.1007/978-0-8176-4523-6Suche in Google Scholar
[18] N. M. Katz, On the calculation of some differential Galois groups, Invent. Math. 87 (1987), no. 1, 13–61. 10.1007/BF01389152Suche in Google Scholar
[19] N. M. Katz, Exponential sums and differential equations, Ann. of Math. Stud. 124, Princeton University, Princeton 1990. 10.1515/9781400882434Suche in Google Scholar
[20] M. Kontsevich and Y. Soibelman, Cohomological Hall algebra, exponential Hodge structures and motivic Donaldson–Thomas invariants, Commun. Number Theory Phys. 5 (2011), no. 2, 231–352. 10.4310/CNTP.2011.v5.n2.a1Suche in Google Scholar
[21] Y. Matsui and K. Takeuchi, Monodromy at infinity of polynomial maps and Newton polyhedra (with an appendix by C. Sabbah), Int. Math. Res. Not. IMRN 2013 (2013), no. 8, 1691–1746. 10.1093/imrn/rns092Suche in Google Scholar
[22] T. Mochizuki, Twistor property of GKZ-hypergeometric systems, preprint (2015), https://arxiv.org/abs/1501.04146. Suche in Google Scholar
[23] S. Patrikis and R. Taylor, Automorphy and irreducibility of some l-adic representations, Compos. Math. 151 (2015), no. 2, 207–229. 10.1112/S0010437X14007519Suche in Google Scholar
[24] Y. Qin, L-functions of Kloosterman sheaves, preprint (2023), https://arxiv.org/abs/2305.04882. Suche in Google Scholar
[25] C. Sabbah, An explicit stationary phase formula for the local formal Fourier–Laplace transform, Singularities I, Contemp. Math. 474, American Mathematical Society, Providence (2008), 309–330. 10.1090/conm/474/09262Suche in Google Scholar
[26] C. Sabbah, Fourier–Laplace transform of a variation of polarized complex Hodge structure, II, New developments in algebraic geometry, integrable systems and mirror symmetry, Adv. Stud. Pure Math. 59, Mathematical Society of Japan, Tokyo (2010), 289–347. 10.2969/aspm/05910289Suche in Google Scholar
[27] C. Sabbah, Irregular Hodge theory. With the collaboration of Jeng-Daw Yu, Mém. Soc. Math. Fr. (N. S.) (2018), no. 156, 1–126. 10.24033/msmf.464Suche in Google Scholar
[28] C. Sabbah and J.-D. Yu, On the irregular Hodge filtration of exponentially twisted mixed Hodge modules, Forum Math. Sigma 3 (2015), Paper No. e9. 10.1017/fms.2015.8Suche in Google Scholar
[29] C. Sabbah and J.-D. Yu, Hodge properties of Airy moments, Tunis. J. Math. 5 (2023), no. 2, 215–271. 10.2140/tunis.2023.5.215Suche in Google Scholar
[30] M. Saito, Modules de Hodge polarisables, Publ. Res. Inst. Math. Sci. 24 (1988), no. 6, 849–995. 10.2977/prims/1195173930Suche in Google Scholar
[31] M. Saito, Mixed Hodge modules, Publ. Res. Inst. Math. Sci. 26 (1990), no. 2, 221–333. 10.2977/prims/1195171082Suche in Google Scholar
[32] C. A. Weibel, An introduction to homological algebra, Cambridge Stud. Adv. Math. 38, Cambridge University, Cambridge 1994. 10.1017/CBO9781139644136Suche in Google Scholar
[33] J.-D. Yu, Irregular Hodge filtration on twisted de Rham cohomology, Manuscripta Math. 144 (2014), no. 1–2, 99–133. 10.1007/s00229-013-0642-xSuche in Google Scholar
[34] Z. Yun, Galois representations attached to moments of Kloosterman sums and conjectures of Evans. Appendix B by Christelle Vincent, Compos. Math. 151 (2015), no. 1, 68–120. 10.1112/S0010437X14007593Suche in Google Scholar
© 2024 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- Gluing Karcher–Scherk saddle towers I: Triply periodic minimal surfaces
- Nodal Enriques surfaces are Reye congruences
- Multi-localized time-symmetric initial data for the Einstein vacuum equations
- Matrix representations of arbitrary bounded operators on Hilbert spaces
- Hodge numbers of motives attached to Kloosterman and Airy moments
- Products of primes in arithmetic progressions
- A quantitative stability result for the sphere packing problem in dimensions 8 and 24
- Bounds on Cheeger–Gromov invariants and simplicial complexity of triangulated manifolds
Artikel in diesem Heft
- Frontmatter
- Gluing Karcher–Scherk saddle towers I: Triply periodic minimal surfaces
- Nodal Enriques surfaces are Reye congruences
- Multi-localized time-symmetric initial data for the Einstein vacuum equations
- Matrix representations of arbitrary bounded operators on Hilbert spaces
- Hodge numbers of motives attached to Kloosterman and Airy moments
- Products of primes in arithmetic progressions
- A quantitative stability result for the sphere packing problem in dimensions 8 and 24
- Bounds on Cheeger–Gromov invariants and simplicial complexity of triangulated manifolds