Hélène Esnault
List of publications.
Thèse de Doctorat de 3◦ cycle :Singularités rationnelles et groupes algébriques. Université Paris VII, October 1976
Thèse de Doctorat d’Etat :corresponds to the publications 3 - 6, Université Paris VII, Feb. 1984
Publications:

References[1] Sur l’identification de singularités apparaissant dans des groupes algébriques complexes. Publ.
Math. de l’Université Paris VII, 7 (1979), 31 - 59(résumé of the ”Thèse de 3◦ cycle”).
[2] Classification des variétés de dimension 3 et plus. Séminaire Bourbaki, exp 568, Fév 81. Springer
Lect. Notes in Math. 901, 111 - 131, (survey).
[3] Fibre de Milnor d’un cône sur une courbe plane singulière. Inventiones math. 68 (1982), 477 496.
[4] (with E. Viehweg) Revêtement cycliques. Algebraic Threefolds, Proc. Varenna 1981, Springer
Lect. Notes in Math. 947, 241 - 250, (survey).
[5] (with E. Viehweg) Sur une minoration du degré d’hypersurfaces s’ annulant en certain points.
Math. Ann. 263 (1983), 75 - 86.
[6] (with E. Viehweg) Dyson’s lemma for polynomials in several variables (and the theorem of Roth).
Inventiones math. 78 (1984), 445 - 490.
[7] (with E. Viehweg) Two dimensional quotient singularities deform to quotient singularities. Math.
Ann. 271 (1985), 439 - 449.
[8] Reflexive modules on quotient surface singularities. Journ. reine angew. Math. 362 (1985), 63 71.
[9] (with E. Viehweg) Revêtements cycliques II. Proc. Algebraic Geometry,
La Rabida 1984, Hermann, Travaux en cours 23 (1987), 81 - 96.
[10] (with H. Knörrer) Reflexive modules over rational double points.
Math. Ann. 272 (1985), 545 - 548.
[11] (with E. Viehweg) Logarithmic De Rham complexes and vanishing theorems. Inventiones math.
86 (1986), 161 - 194.
[12] Characteristic classes of flat bundles. Topology 27 (1988), 323 - 352.
[13] (with E. Viehweg) Deligne-Beilinson cohomology. In: Beilinson’s Conjectures on Special Valuesof L-Functions ( Ed.: Rapoport, Schappacher, Schneider ). Perspectives in Math. 4, Academic
Press (1988), 43 - 91.
[14] (with E. Viehweg) A remark on a non-vanishing theorem of P. Deligne and G.T. Mostow. Journ.
reine angew. Math. 381 (1987), 211 - 213.
[15] (with E. Viehweg) Vanishing and non-vanishing theorems. Proc. Hodge Theory, Luminy 1987
(Ed.: Barlet, Elzein, Esnault, Verdier, Viehweg). Astérisque 179-180 (1989), 97 - 112.
[16] On the Loday symbol in the Deligne-Beilinson cohomology.
K-Theory 3 (1989), 1 - 28.
[17] A note on the cycle map. Journal reine angew. Math. 411 (1990), 51 - 65.
[18] (with E. Viehweg) Effective bounds for semipositive sheaves and the height of points on curves
over complex function fields. Compositio math., 76 (1990), 69 - 85.
[19] A regulator map on singular varieties. Math. Ann. 286 (1990), 169 - 191.
[20] Une remarque sur la cohomologie du faisceau de Zariski de la K-théorie de Milnor sur une variétélisse complexe. Math. Zeitschrift 205 (1990), 373 - 378.
1

[21] Some examples of computation of a regulator map on singular varieties. Contemporary Mathematics, 131 (1992) (Part 3), 399-417 , Proc. of the ”A.I. Maltsev Conf.” on Algebra and Analysis,
Novosibirsk 1989.
[22] Hodge type of subvarieties of P n of small degrees. Math. Ann. 288 (1990), 549 - 551.
[23] (with E. Viehweg) Ample sheaves on moduli schemes. ”Proceedings of the Conference in Algebraic and Analytic Geometry”, Tokyo, (1990), ICM 90, Lecture Notes, 53 - 80.
[24] (with J. Seade and E. Viehweg) Characteristic divisors on complex manifolds. Journ. reine
angew. Math. 424 (1992), 17-30[25] (with V. Srinivas) Chern classes of vector bundles with holomorphic connections on a completesmooth complex variety. Journal of Diff. Geometry, 36 (1992), 257-267.
[26] (with V. Schechtman and E. Viehweg) Cohomology of local systems on the complement ofhyperplanes. Inventiones math. 109 (1992), 557-561. Erratum: Inventiones math. 112 (1993),
447.
[27] (with M. V. Nori and V. Srinivas) Hodge type of projective varieties of low degree. Math. Ann.
293 (1992), 1-6.
[28] (with E. Viehweg) Lectures on Vanishing Theorems. Book. DMV-Seminar Band 20, Birkhäuser,
164 pages.
[29] (with B. Kahn and E. Viehweg) Coverings of odd degree and Stiefel-Whitney classes. Journ.
reine angew. Math. 441 (1993), 145-188.
[30] (with E. Viehweg) Higher Kodaira-Spencer classes. Math. Ann. 299 (1994), 491-527.
[31] Characteristic classes of flat bundles, II. K-Theory 6 (1992), 45-56.
[32] (with M. Levine) Surjectivity of cycle maps. In Journées de Géométrie Algébrique d’Orsay, Juillet
1992, Astérisque 218 (1993), 203-226.
[33] (with V. Srinivas and E. Viehweg) Decomposability of Chow groups implies decomposability ofcohomology. In Journées de Géométrie Algébrique d’Orsay, Juillet 1992, Astérisque 218 (1993),
227-242.
[34] (with K. Paranjape) Remarks on absolute de Rham and absolute Hodge cycles. C. R. Acad. Sc.
Paris, t. 319, Série I (1994) 67-72.
[35] Coniveau of classes of flat bundles trivialized on a smooth covering of a complex manifold.
K-Theory 8 (1994), 483-488[36] (with K. Corlette) Classes of local systems of Q hermitian vector spaces. Preprint 1994, 6 pages,
appendix to ”Riemann-Roch for flat bundles” by J.-M. Bismut, Chinese Annals of Mathematics
26B:1 (2005), 15-44.
[37] (with S. Bloch) The coniveau filtration and non- divisibility for algebraic cycles. Math. Ann. 304(1996), 303-314.
[38] (with M. Levine and E. Viehweg) Chow groups on projective varieties of very small degree. Duke
Math. J. 87 (1997), 29-58.
[39] (with S. Bloch) Algebraic Chern-Simons theory. Am. J. of Mathematics 119 (1997), 903-952.
[40] Recent developments on characteristic classes of flat bundles on complex algebraic manifolds.
Jber. d. Dt. Math.-Verein. 98 (1996), 182-191, (survey).
[41] (with B. Kahn, M. Levine, E. Viehweg) The Arason invariant and mod 2 algebraic cycles. Journalof the American Mathematical Society 11 (1998), 73-118.
[42] Algebraic Differential Characters. In Regulators in Analysis, Geometry and Number Theory,
Progress in Mathematics, Birkhäuser Verlag, 171 (2000), 89-117.
[43] A remark on an algebraic Riemann-Roch formula for flat bundles. K-Theory 13 (1998), 61-68.
[44] (with V. Srinivas, E. Viehweg) The universal regular quotient of the Chow group of 0-cycles ona singular projective variety. Inventiones math. 135 (1999), 595-664.
[45] (with E. Viehweg) Germs of de Rham cohomology classes which vanish at the generic point. C.
R. Acad. Sci. Paris 326 (1998) 857-862.
[46] Algebraic theory of characteristic classes of bundles with connection. In Algebraic K-theory,
Proceedings of Symposia in pure Mathematics 67 (1999), 13-25.
[47] (with S. Bloch) A Riemann-Roch theorem for flat bundles, with values in the algebraic ChernSimons theory. Annals of Mathematics 151 (2000), 1-46.
[48] (with E. Viehweg) Semistable bundles on curves and irreducible representations of the fundamental group. Algebraic Geometry: Hirzebruch 70, Contemporary Mathematics 241 (1999),129-141.

[49] (with S. Bloch) Lectures on Algebro-Geometric Chern-Weil and Cheeger-Chern-Simons Theory
for Vector Bundles. In Arithmetic and Geometry of Algebraic Cycles. Nato Science Series 548(2000), 3-29.
[50] (with S. Bloch) Gauß-Manin determinants of rank 1 irregular connection on curves. Math. Ann.
321 (2001), 15-87, with an addendum: the letter of P. Deligne to J.-P. Serre (Feb. 74) on
ϵ-factors, 65-87.
[51] (with M. Levine) The Steinberg curve. Am. J. of Mathematics 122 (2000), 783-804.
[52] (with I.H. Tsai) Determinant bundle in a family of curves, after A. Beilinson and V. Schechtman.
Comm. Math. Phys. 211 (2000), 359-363.
[53] (with S. Bloch) Relatives Algebraic Characters. In Motives, Polylogarithms and Hodge Theory,
International Press Lecture Series, vol. 3, part I (2002), 47-75.
[54] (with S. Bloch) Gauß-Manin determinant connections and periods for irregular connections.
Geom. funct. anal. Special Volume-GAFA 2000, 1-31, Birkhäuser Verlag.
[55] (with S. Bloch) A formula for Gauß-Manin determinants. Preprint 2000, 37 pages.
[56] (with S. Bloch) Homology for irregular connections. Journal de Théorie des Nombres de Bordeaux
16 (2004) no 2, 357-371.
[57] (with C. Hertling) Semistable bundles and reducible representations of the fundamental group.
International Journal of Mathematics 12, no7 (2001), 847-855.
[58] (with A. Beilinson and S. Bloch) ϵ-factors for Gauß- Manin determinants. Moscow Mathematical
Journal, 2 no 3 (2002), 1-56.
[59] (with S. Bloch) An additive version of higher Chow groups. Annales Scientifiques de l’École
Normale Supérieure, 36 (4) (2003), 463-477.
[60] (with E. Viehweg) Chern classes of Gauß-Manin bundles of weight 1 vanish. K-Theory 26 (2002),
287-305.
[61] Characteristic classes of flat bundles and determinant of the Gauß-Manin connection. Proceedingsof the International Congress of Mathematicians, Beijing 2002, Higher Education Press, 471-483.
[62] Varieties over a finite field with trivial Chow group of 0-cycles have a rational point. Inventiones
math. 151 (2003), 187-191.
[63] (with S. Bloch) The additive dilogarithm. Documenta mathematica, Extra Volume: Kazuya
Kato’s Fiftieth Birthday (2003), 131-155.
[64] (with D. Wan) Hodge type of the exotic cohomology of complete intersections. C. R. Acad. Sci.
Paris, Ser. I 336 (2003), 153-157.
[65] (with S. Bloch) Congruences for the number of rational points, Hodge type and motivic conjectures for Fano varieties. Cubo A Mathematical Journal, 05, no 03 (2003), 251-262.
[66] (with S. Bloch and M. Levine) Decomposition of the diagonal and eigenvalues of Frobenius for
Fano hypersurfaces. Am. J. of Mathematics, 127 no1 (2005), 193-207.
[67] Eigenvalues of Frobenius acting on the ℓ-adic cohomology of complete intersections of low degree.
C. R. Acad. Sci. Paris, Ser. I 337 (2003), 317-320.
[68] (with N. Katz) Cohomological divisibility and point count divisibility. Compositio math. 141 01(2005), 93-100.
[69] (with A. Beilinson, S. Bloch, P. Deligne) Periods for irregular connections on curves. Preprint
2003, 59 pages.
[70] Some elementary theorems about divisibility of 0-cycles on abelian varieties defined over finite
fields. International Mathematics Research Notices 19 (2004), 929-935.
[71] (with S. Bloch) Local Fourier transforms and rigidity for D-modules. Asian Journal of Mathematics, special issue dedicated to Armand Borel, Vol. 8, No 4 (2004), 587-606.
[72] Appendix to “ Congruences for rational points on varieties over finite fields” by N. Fakhruddin
and C. S. Rajan. Math. Ann. 333 (2005), 811-814.
[73] Deligne’s integrality theorem in unequal characteristic and rational points over finite fields.
Annals of Mathematics 164 (2006), 715-730.
[74] (with P. Deligne) Appendix to “Deligne’s integrality theorem in unequal characteristic and rational points over finite fields”. Annals of Mathematics 164 (2006), 726-730.
[75] Variation of Artin’s vanishing theorem. Advances of Mathematics 198 (2005) issue 2, 435-438,
special issue dedicated to M. Artin.
[76] (with S. Bloch) Künneth projectors and correspondences for open varieties. In Algebraic Cycles
and Motives, vol. 2, 54-72, London Math. Soc. Lecture Note Ser. 344 (2007).

[77] A remark on higher congruences for the number of rational points of varieties defined over afinite field. Preprint 2005, 6 pages.
[78] (with Phùng Hô Hai) The Gauß-Manin connection and Tannaka duality. International Mathematics Research Notices 93878 (2006), 1-35.
[79] (with S. Bloch and D. Kreimer) On motives attached to graph polynomials. Comm. Math. Phys.
267 no1 (2006), 181-225.
[80] (with P. Berthelot and S. Bloch) On Witt vector cohomology for singular varieties. Compositio
math. 143 (2007), 363-392.
[81] (with M. Blickle and K. Rülling) Characteristic 0 and p analogies, and some motivic cohomology.
In Global Aspects of Complex Geometry, ed. Catanese, Esnault, Huckelberry, Hulek, Peternell,
Springer Verlag (2006), 59-82.
[82] (with M. Blickle) Rational singularities and rational points. Pure Appl. Math. Q. 4 (2008), no.
3, part 2, 729–741.
[83] (with Phùng Hô Hai and X. Sun) On Nori’s Fundamental Group Scheme. Progress in Mathematics, Vol. 265 (2007), 377-398.
[84] Partial connection for p-torsion line bundles in characteristic p > 0. Inspired by S. S. Chern,
173–178, Nankai Tracts Math. 11, World Sci. Publ. Hackensack, NJ (2006).
[85] (with Phùng Hô Hai) The fundamental groupoid scheme and applications. Annales de l’Institut
Fourier 58 (2008), 2381-2412.
[86] (with Phùng Hô Hai) Packets in Grothendieck’s Section Conjecture. Advances in Mathematics
218 (2008), 395-416.
[87] Coniveau over p-adic fields and points over finite fields. C. R. Acad. Sci. Paris, Ser. I 345 (2007)
73-76.
[88] (with C. Xu) Congruence for rational points over finite fields and coniveau over local fields.
Transactions of the AMS 361 (2009), 2679-2688.
[89] (with M. Levine) Tate motives and fundamental group. Preprint 2007, 65 pages.
[90] (with A. Ogus) Hodge cohomology of invertible sheaves, in Motives and Algebraic Cycles, A
Celebration in Honour of Spencer J. Bloch, American Mathematical Society, Fields Institute, 56(2009), 83–91.
[91] Algebraic differential characters of flat connections with nilpotent residues. In Algebraic Topology, Abel Prisen 4 (2007), Springer Verlag, 83–94.
[92] (with O. Wittenberg) Remarks on the cycle classes of sections of the arithmetic fundamentalgroup. Moscow Mathematical Journal 9 no3 (2009), 1-17.
[93] (with O. Wittenberg) On abelian birational sections. Journal of the American MathematicalSociety 23 (2010), 713–724.
[94] (with Phùng Hô Hai) Two small remarks on Nori fundamental group scheme. Advanced Studies
in Pure Mathematics 60 (2010), 237–243.
[95] (with V. Mehta) Simply connected projective manifolds in characteristic p > 0 have no nontrivial
stratified bundles. Inventiones math. 181 (2010), 449–465.
[96] (with E. Viehweg) On a rationality question in the Grothendieck ring of varieties. Acta Mathematica Vietnamica 35 (1) (2010), 31–41.
[97] (with V. Mehta) Weak Density of the Fundamental Group Scheme. International Mathematics
Research Notcies 13 (2011), 3071–3081.
[98] (with E. Viehweg) Surface singularities dominated by smooth varieties. Journ. reine angew.
Math. 649 (2010), 1–9.
[99] (with A. Hogadi) On the algebraic fundamental group of smooth varieties in characteristic p > 0.
Transactions of the AMS 364 (2012), 2429–2442.
[100] (with P. Berthelot and K. Rülling) Rational points over finite fields for regular models of algebraic
varieties of Hodge type ≥ 1. Annals of Mathematics 176 (2012), 1–96.
[101] (with J. Nicaise) Finite group actions, rational fixed points and weak Néron models. Pure Applied
Math. Q. 7:4 in the Special issue in memory of Eckart Viehweg (2011), 1209–1240.
[102] (with V. Srinivas) Algebraic versus topological entropy for surfaces over finite fields. Osaka J.
Math. 50 (2013) no3, 827–846.
[103] (with M. Kerz) Notes on Deligne’s letter to Drinfeld dated Marc 5, 2007. Preprint 2011, 19
pages. Not for publication.

[104] (with A. Langer) On a positive equicharacteristic variant of the p-curvature conjecture. Documenta mathematica 18 (2013), 23–50.
[105] (with X. Sun) Stratified bundles and étale fundamental group. Ann. Sc. Norm. Pisa Cl. Sci. (5)XIII (2014), 1–18.
[106] (with S. Bloch and M. Kerz) p-adic deformation of algebraic cycle classes. Inventiones math.
195, issue 3 (2014), 673–722.
[107] On flat bundles in characteristic 0 and p > 0. European Congress of Mathematics, Kraków, 2-7
July, 2012, European Mathematical Society, 301–313.
[108] (with M. Levine and O. Wittenberg) Index of varieties over Henselian fields and Euler characteristic of coherent sheaves. J. Algebraic Geometry 24 (2015), 693–718.
[109] (with M. Kerz) A finiteness theorem for Galois representations of function fields over finite fields(after Deligne). Acta Mathematica Vietnamica 37 4 (2012), 531–562.
[110] (with C. Sabbah and J.-D. Yu) E1 -degeneration of the irregular Hodge filtration (with an appendix by Morihiko Saito). Journ. reine angew. Mathematik 729 (2017), 171–227.
[111] (with O. Wittenberg) On the cycle class map for 0-cycles over local fields. Annales Scientifiquesde l’École Normale Supérieure 49 (4) (2016), 481–518.
[112] (with S. Bloch and M. Kerz) Deformation of algebraic cycle classes in characteristic 0. Algebraic
Geometry 1 (2014) 3, 290–310.
[113] (with V. Srinivas) Simply connected varieties in characteristic p > 0, with an appendix by
Jean-Benoı̂t Bost. Compositio math. 152 (2016), 255–287.
[114] (with K. Oguiso) Non-liftability of automorphism groups of a K3 surface in positive characteristic. Math. Ann. 363 (2015), 1187–1206.
[115] (with K. Oguiso and X. Yu) Automorphisms of elliptic K3 surfaces and Salem numbers of
maximal degree. Algebraic Geometry 3 (2016), 496–507.
[116] (with A. Shiho) Convergent isocrystals on simply connected varieties. Annales de l’Institut
Fourier 68 (2018) no 5, 2019–2148.
[117] (with M. Kerz and O. Wittenberg) A restriction isomorphism for cycles of relative dimension
zero. Cambridge Journal of Mathematics, 4 2 (2016), 163–196.
[118] (with L. Kindler) Lefschetz theorems for tamely ramified coverings. Proc. of the AMS 144 (2016),
5071–5080.
[119] (with A. Shiho) Chern classes of crystals. Transactions of the AMS 371 (2) (2019), 1333–1358.
[120] Some fundamental groups in arithmetic geometry. Proceedings of Symposia in Pure Mathematics
97.2 (2018), Algebraic Geometry Salt Lake City 2015, AMS, 169–179.
[121] A remark on Deligne’s finiteness theorem. International Mathematics Research Notices, 16(2017), 4962–4970.
[122] Survey on some aspects of Lefschetz theorems in algebraic geometry. Revista Mathemática Complutense 30 (2) (2017), 217–232.
[123] (with T. Abe) A Lefschetz theorem for overconvergent isocrystals with Frobenius structure.
Annales Scientifiques de l’École Normale Supérieure 52 (4) (2019), 1243–1264.
[124] (with M. Kisin) D-modules and finite monodromy. Selecta Mathematica, volume dedicated toAlexander Beilinson 24 (2018) (1), 145–155.
[125] (with M. Harris) Chern classes of automorphic bundles. Pure and Applied Mathematics Quarterly
13 2 (2017), 193–213.
[126] (with M. Groechenig) Rigid connections, F -isocrystals and p-curvature. Acta Mathematica 225
1 (2020), 103–158.
[127] (with V. Srinivas) A relative version of Gieseker’s problem on stratifications in characteristicp > 0. International Mathematics Research Notices 18 (2019), 5635–5648.
[128] (with M. Groechenig) Cohomologically rigid local systems and integrality. Selecta Mathematica
24 (2018) (5), 4279–4292.
[129] (with M. Harris) Chern classes of automorphic vector bundles, II, 28 pages. Épijournal deGéométrie Algébrique 3 (2019), article 14.
[130] Cohomological dimension in pro-p-towers. International Mathematics Research Notices 2021 8(2021), 5757–5765.
[131] (with L. Kindler and V. Srinivas) A note on fierce ramification. J. of Algebra 528 (2019), 250–259.
[132] (with C. Sabbah) Good lattices of algebraic connections. Documenta mathematica 24 (2019),
271–301.

[133] (with M. Kerz) Arithmetic subspaces of moduli spaces of rank one local systems. Cambridge
Journal of Mathematics 8 (2020) (3), 453–478.
[134] (with M. Kerz) Étale cohomology of rank one ℓ-adic local systems in positive characteristic.
Selecta Mathematica 27 (2021) no 4, paper no 58, 25 pages.
[135] Survey on special subloci of the moduli spaces of local systems on complex varieties. Preprint
2019, 8 pages, to appear in Proceedings of the International Congress of Chinese Mathematicians(Beijing 2019).
[136] (with M. Kerz) Density of Arithmetic Representations of Function Fields. Épijournal deGéométrie Algébrique 6 (2022), article no. 5.
[137] Remembering Steve Zucker. Notices Amer. Math. Soc. 68 (2021) no7, 1156–1172, (1162–1163).
[138] (with V. Srinivas) Bounding ramification by covers and curves, in Nine mathematical challenges,
Proceedings of Symposia in Pure Math, AMS 104 (2021), 31–43.
[139] (with M. D’Addezio) On the universal extensions in Tannakian categories. International Mathematics Research Notices 18 (2022), 14008–14033.
[140] (with M. Kerz) Local systems with quasi-unipotent monodromy at infinity are dense. Israel
Journal of Mathematics 257 (2023), 251–262.
[141] (with M. Shusterman and V. Srinivas) Finite presentation of the tame fundamental group. Selecta
Mathematica 28 (2022) no 2, paper no 37, 19 pages.
[142] (with V. Srinivas and J. Stix) An obstruction to lifting to characteristic 0. Algebraic Geometry
10 (2023) no 3, 327–347.
[143] (with M. Groechenig) Frobenius structures and unipotent monodromy at infinity. Preprint 2021,
8 pages; Appendix to ’André-Oort for Shimura varieties’ by J. Pila, Ananth Shankar, J. Tsimerman, 25 pages.
[144] (with D. Wan) Divisibility of Frobenius eigenvalues on ℓ-adic cohomology. Proceedings Indian
Acad. Sci. Mathematical Sci. 132 (2002) 2, Paper 60.
[145] (with J. de Jong and M. Groechenig) Rigid non-cohomologically rigid local systems. Algebraic
Geometry and Phyiscs 1 (2023).
[146] (with J. de Jong) Integrality of the Betti moduli space. Transactions of the AMS 377 (1) (2024),
431–448.
[147] Lectures on Local Systems in Algebraic-Arithmetic Geometry. Lecture Notes in Mathematics
2337 (2023), Springer Verlag, i-vii + 96 pp.
[148] Some Arithmetic Properties of Complex Local Systems. Notices Amer. Math. Soc. 70 (2023)
no11, 1793–1801.
[149] Rational Points over C1 fields, preprint 2023, 9 pages, to appear in the Springer volume inmemory of Manin.
[150] (with M. Groechenig) Crystallinity of rigid flat connections revisited, preprint 2023, 26 pages,
appears in Selecta Mathematica.
[151] (with M. Kerz) Semi-stable Lefschetz pencils, preprint 2023, 46 pages.
[152] (with M. Kerz) A non-abelian version of Deligne’s Fixed Part Theorem, preprint 2024, 23 pages.