Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Infinitesimal local study of formal schemes   We make a systematic study of the infinitesimal lifting conditions of a
pseudo finite type map of noetherian formal schemes. We recover the usual
general properties in this context, and, more importantly, we uncover some new
phenomena. We define a completion map of formal schemes as the one that arises
canonically by performing the completion of a noetherian formal scheme along a
subscheme, following the well-known pattern of ordinary schemes. These maps are
etale in the sense of this work (but not adic). They allow us to give a local
description of smooth morphisms. This morphisms can be factored locally as a
completion map followed from a smooth adic morphism. The latter kind of
morphisms can be factored locally as an etale adic morphism followed by a
(formal) affine space. We also characterize etale adic morphisms giving an
equivalence of categories between the category of etale adic formal schemes
over a noetherian formal scheme (X, O_X) and the category of etale schemes over
the ordinary scheme (X, O_X/I), with I an Ideal of definition. These results
characterize completely the local behavior of formally smooth pseudo finite
type (i.e. smooth) maps of noetherian formal schemes. In the final chapter, we
study the basic deformation theory of smooth morphisms.

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The categories of this paper are: funct-an
11
The categories of this paper are: hep-lat
36
The categories of this paper are: cmp-lg
25
The categories of this paper are: patt-sol
0
The categories of this paper are: hep-ph
1
The categories of this paper are: cs
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The categories of this paper are: eess
34
The categories of this paper are: chem-ph
6
The categories of this paper are: astro-ph
26
The categories of this paper are: bayes-an
5
The categories of this paper are: gr-qc
10
The categories of this paper are: q-bio
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The categories of this paper are: nlin
13
The categories of this paper are: quant-ph
4
The categories of this paper are: cond-mat
15
The categories of this paper are: nucl-ex