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Zbl 0969.14015
Gillet, Henri; Soulé, Christophe
Direct images in non-archimedean Arakelov theory. (English)
[J] Ann. Inst. Fourier 50, No.2, 363-399 (2000). ISSN 0373-0956; ISSN 1777-5310/e

An earlier paper by {\it S. Bloch, H. Gillet}, and {\it C. Soulé} [J. Algebr. Geom. 4, No. 3, 427-485 (1995; Zbl 0866.14011)] constructed a theory for a variety $X$ over a number field that does at finite places what the Arakelov-Gillet-Soulé intersection theory does at infinite places of the number field. For example, this earlier paper found non-Archimedean analogs of the groups of $C^\infty$ forms on $X(\Bbb C_v)$; these are central to Gillet-Soulé intersection theory at infinite places. \par The present paper fills in one notable omission in that earlier paper: an analogue of the Riemann-Roch-Grothendieck theorem in this context. The starting point is the definition of a direct image that respects base change and change of model. For this definition, the authors then define Grothendieck groups and higher analytic torsion currents, leading up to a Riemann-Roch theorem for this direct image.
[P.Vojta (Berkeley)]

MSC 2000:: *14G40 Arithmetic varieties and schemes
14C40 Riemann-Roch theorems
14G20 p-adic ground fields
14C15 Rational equivalence rings

Keywords: Arakelov theory; Riemann-Roch-Grothendieck theorem; arithmetic Chow groups; direct image; intersection theory

Citations: Zbl 0866.14011

Cited in: Zbl 0976.14024

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