Gangopadhyay, Chandranandan; Sebastian, Ronnie Fundamental group schemes of some Quot schemes on a smooth projective curve. (English) Zbl 1441.14151 J. Algebra 562, 290-305 (2020). Summary: Let \(k\) be an algebraically closed field. Let \(C\) be an irreducible smooth projective curve over \(k\). Let \(E\) be a locally free sheaf on \(C\) of rank \(\geq 2\). Fix an integer \(d \geq 2\). Let \(\mathcal{Q}\) denote the Quot scheme parameterizing torsion quotients of \(E\) of degree \(d\). In this article we compute the \(S\)-fundamental group scheme of \(\mathcal{Q} \). Cited in 3 Documents MSC: 14L15 Group schemes 14C05 Parametrization (Chow and Hilbert schemes) 14J60 Vector bundles on surfaces and higher-dimensional varieties, and their moduli 14F35 Homotopy theory and fundamental groups in algebraic geometry Keywords:finite vector bundle; \(S\)-fundamental group scheme; Hilbert scheme; semistable bundle; Tannakian category PDFBibTeX XMLCite \textit{C. Gangopadhyay} and \textit{R. Sebastian}, J. Algebra 562, 290--305 (2020; Zbl 1441.14151) Full Text: DOI arXiv References: [1] Biswas, Indranil; Dhillon, Ajneet; Hurtubise, Jacques, Brauer groups of Quot schemes, Mich. Math. J., 64, 3, 493-508 (2015) · Zbl 1327.14097 [2] Biswas, Indranil; Hogadi, Amit, On the fundamental group of a variety with quotient singularities, Int. Math. Res. Not., 5, 1421-1444 (2015) · Zbl 1326.14052 [3] Bertone, Cristina; Kleiman, Steven L.; Roggero, Margherita, On the quot scheme \(\operatorname{Quot}_{\mathcal{O}_{\mathbb{P}^1}^r / \mathbb{P}^1 / k}^d (2019)\) [4] Biswas, Indranil; Parameswaran, A. J.; Subramanian, S., Monodromy group for a strongly semistable principal bundle over a curve, Duke Math. J., 132, 1, 1-48 (2006) · Zbl 1106.14032 [5] Deligne, Pierre; Milne, James S.; Ogus, Arthur; Shih, Kuang-yen, Hodge Cycles, Motives, and Shimura Varieties, 101-228 (1982), Springer-Verlag: Springer-Verlag Berlin-New York, (Chapter 2) · Zbl 0465.00010 [6] Fantechi, Barbara; Göttsche, Lothar; Illusie, Luc; Kleiman, Steven L.; Nitsure, Nitin; Vistoli, Angelo, Fundamental Algebraic Geometry, Mathematical Surveys and Monographs, vol. 123 (2005), American Mathematical Society: American Mathematical Society Providence, RI, Grothendieck’s FGA explained · Zbl 1085.14001 [7] Hartshorne, Robin, Algebraic Geometry, Graduate Texts in Mathematics, vol. 52 (1977), Springer-Verlag: Springer-Verlag New York-Heidelberg · Zbl 0367.14001 [8] Hogadi, Amit; Mehta, Vikram, Birational invariance of the S-fundamental group scheme, Special Issue: In Memory of Eckart Viehweg. Special Issue: In Memory of Eckart Viehweg, Pure Appl. Math. Q., 7, 4, 1361-1369 (2011) · Zbl 1316.14028 [9] Langer, Adrian, On the S-fundamental group scheme, Ann. Inst. Fourier (Grenoble), 61, 5, 2077-2119 (2012), (2011) · Zbl 1247.14019 [10] Langer, Adrian, On the S-fundamental group scheme. II, J. Inst. Math. Jussieu, 11, 4, 835-854 (2012) · Zbl 1252.14028 [11] Matsumura, Hideyuki, Commutative Ring Theory, Cambridge Studies in Advanced Mathematics, vol. 8 (1986), Cambridge University Press: Cambridge University Press Cambridge, translated from the Japanese by M. Reid · Zbl 0603.13001 [12] Nori, Madhav V., On the representations of the fundamental group, Compos. Math., 33, 1, 29-41 (1976) · Zbl 0337.14016 [13] Nori, Madhav V., The fundamental group-scheme, Proc. Indian Acad. Sci. Math. Sci., 91, 2, 73-122 (1982) · Zbl 0586.14006 [14] Paul, Arjun; Sebastian, Ronnie, Fundamental group schemes of n-fold symmetric product of a smooth projective curve (2019) [15] Paul, Arjun; Sebastian, Ronnie, Fundamental group schemes of Hilbert scheme of n points on a smooth projective surface (2019) [16] The Stack Project This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.