Green forms and their product. Duke Math. J. 75 (1994), no. 3, 529–574. (for a preliminary version see chapter II of PhD thesis)
Arithmetic Chow rings and Deligne-Beilinson cohomology. J. Algebraic Geom. 6 (1997), no. 2, 335–377.(for a preliminary version see chapter III of PhD thesis)
(with Wang) Higher Bott-Chern forms and Beilinson’s regulator. Invent. Math. 132 (1998), no. 2, 261–305 (el)
MR1738857 (2001k:14023) Burgos Gil, José I. Hermitian vector bundles and characteristic classes. The arithmetic and geometry of algebraic cycles (Banff, AB, 1998), 155–182, CRM Proc. Lecture Notes, 24, Amer. Math. Soc., Providence, RI, 2000.
MR1872772 Burgos Gil, José I. An introduction to Arakelov theory. (Catalan) Butl. Soc. Catalana Mat. 16 (2001), no. 1, 61–85. 14G40 (14-02)
MR1869655 (2002m:19002) Burgos Gil, José I. The regulators of Beilinson and Borel. CRM Monograph Series, 15. American Mathematical Society, Providence, RI, 2002. xii+104 pp. ISBN: 0-8218-2630-1.pdf preliminary version
MR1968898 (2004c:14013) Burgos, José I.; Wildeshaus, Jörg Modules de Hodge sur les variétés de Shimura, et leur dégénérescence dans la compactification de Baily-Borel. (French) [Hodge modules on Shimura varieties, and their degeneration in the Baily-Borel compactification] C. R. Math. Acad. Sci. Paris 336 pdf.
MR2060481 (2005e:14039) Burgos, José I.; Wildeshaus, Jörg Hodge modules on Shimura varieties and their higher direct images in the Baily-Borel compactification. Ann. Sci. École Norm. Sup. (4) 37 (2004), no. 3, 363–413.pdf.
MR2218402 (2007e:14039) Burgos Gil, J. I.; Kramer, J.; Kühn, U. Arithmetic characteristic classes of automorphic vector bundles. Doc. Math. 10 (2005), 619–716 (electronic). pdf.
MR2285241 Burgos Gil, J. I.; Kramer, J.; Kühn, U. Cohomological arithmetic Chow rings. J. Inst. Math. Jussieu 6 (2007), no. 1, 1–172.
nLab page on Burgos Gil
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Andreas Holmström