Extension of some notions from the theory of schemes to the theory of formal schemes

1971 ◽  
pp. 44-51
Author(s):  
Alexander Grothendieck ◽  
Jacob P. Murre
Keyword(s):  
Formal Schemes

scholarly journals Weak Formal Schemes

1972 ◽  
Vol 45 ◽  
pp. 1-38 ◽  
Author(s):  
David Meredith
Keyword(s):  
Local Ring ◽  
Maximal Ideal ◽  
Noetherian Local Ring ◽  
Formal Schemes

Throughout this paper, (R, m) denotes a (noetherian) local ring R with maximal ideal m.In [5], Monsky and Washnitzer define weakly complete R-algebras with respect to m. In brief, an R-algebra A† is weakly complete if

scholarly journals The Indispensable Role of Systematic Philosophical Reflection in Scholarship

Phronimon ◽  
2018 ◽  
Vol 18 ◽  
pp. 95-114
Author(s):  
Daniel Francois Strauss
Keyword(s):  
States Of Affairs ◽  
Philosophical View ◽  
Philosophical Reflection ◽  
Formal Schemes ◽  
Constant Change ◽  
Theoretical Thinking ◽  
Philosophical Orientations ◽  
The Relationship ◽  
Systematic Thinking

Sometimes systematic theoretical thinking is identified with abstract (formal) schemes. This opposition is also found in Malan and Goosen’s dismissal of Dooyeweerdian reformational thinking. This article aims at making a contribution to this issue by analysing the indispensable role of systematic philosophical reflection within the world of scholarship. One way in which systematic thinking could be justified is to highlight the need for consistency and the role of logical principles in achieving it. It is argued that, since we are living in the same world, all philosophical orientations have to account for shared states of affairs. At this point attention is given to the question whether or not these “states of affairs” are “static or dynamic.” An alternative for the distinction between static and dynamic is proposed by alternatively considering the relationship between constancy and change. Von Weizsäcker articulates the problem aptly by pointing out that although our experience exhibits constant change, something exists that remains unchanged through all these changes. In conclusion it is pointed out that scholars have only two options: either they give an account of the philosophical presuppositions and systematic distinctions with which they work—in which case they have a philosophical view of reality, or implicitly (and uncritically) they proceed from one or another philosophical view of reality—in which case they are the victims of a philosophical view. The primary aim of this article is, therefore, to highlight the indispensability of systematic thought by referring to some of the main distinctions included in such a system of thought.

Formal schemes for language translations

1972 ◽  
Vol 3 (1-4) ◽  
pp. 17-48 ◽  
Author(s):  
K. Čulík ◽  
C.J.W. Morey
Keyword(s):  
Formal Schemes

scholarly journals Infinitesimal Lifting and Jacobi Criterion for Smoothness on Formal Schemes

2007 ◽  
Vol 35 (4) ◽  
pp. 1341-1367 ◽  
Author(s):  
Leovigildo Alonso Tarrío ◽  
Ana Jeremías López ◽  
Marta Pérez Rodríguez
Keyword(s):  
Formal Schemes

scholarly journals ZERO MODE DIVERGENCE PROBLEM IN STRING THEORY

1994 ◽  
Vol 09 (23) ◽  
pp. 2113-2122
Author(s):  
MAKOTO NATSUUME
Keyword(s):  
String Theory ◽  
Zero Mode ◽  
Wave Packets ◽  
Tree Level ◽  
Formal Schemes ◽  
Divergence Problem ◽  
Formal Procedures

For 2D string theory, the perturbative S-matrices are not well-defined due to a zero mode divergence. Although there exist formal procedures to make the integral convergent, their physical meanings are not clear. We describe a method to obtain finite S-matrices physically to justify the formal schemes. The scheme uses asymptotic states by wave packets which fall faster than exponentials. It is shown that the scheme gives well-defined S-matrices and justifies the formal shifted Virasoro-Shapiro amplitude for simple processes. The tree-level unitarity for these processes is also shown. We point out a problem in this scheme.

scholarly journals The motivic Thom–Sebastiani theorem for regular and formal functions

2018 ◽  
Vol 2018 (735) ◽  
pp. 175-198 ◽  
Author(s):  
Quy Thuong Lê
Keyword(s):  
Analogous Result ◽  
Motivic Integration ◽  
Crucial Element ◽  
Regular Functions ◽  
Formal Schemes ◽  
Theoretic Proof

AbstractThanks to the work of Hrushovski and Loeser on motivic Milnor fibers, we give a model-theoretic proof for the motivic Thom–Sebastiani theorem in the case of regular functions. Moreover, slightly extending Hrushovski–Loeser’s construction adjusted to Sebag, Loeser and Nicaise’s motivic integration for formal schemes and rigid varieties, we formulate and prove an analogous result for formal functions. The latter is meaningful as it has been a crucial element of constructing Kontsevich–Soibelman’s theory of motivic Donaldson–Thomas invariants.

scholarly journals What Is a Good Tomato? A Case of Valuing in Practice

2013 ◽  
Vol 1 (2) ◽  
pp. 125-146 ◽  
Author(s):  
Frank Heuts ◽  
Annemarie Mol
Keyword(s):  
The Netherlands ◽  
Historical Time ◽  
Important Lesson ◽  
Tomato Plants ◽  
Formal Schemes ◽  
Exploratory Inquiry

As a contribution to the field of valuation studies this article lays out a number of lessons that follow from an exploratory inquiry into ‘good tomatoes’. We held interviews with tomato experts (developers, growers, sellers, processors, professional cooks and so-called consumers) in the Netherlands and analysed the transcriptions carefully. Grouping our informants’ concerns with tomatoes into clusters, we differentiate between five registers of valuing. These have to do with money, handling, historical time, what it is to be natural, and sensual appeal. There are tensions between and within these registers that lead to clashes and compromises. Accordingly, valuing tomatoes does not fit into inclusive formal schemes. Neither is it simply a matter of making judgements. Our informants told us how they know whether a tomato is good, but also revealed what they do to make tomatoes good. Their valuing includes activities such as pruning tomato plants and preparing tomato dishes. But if such activities are meant to make tomatoes good, success is never guaranteed. This prompts us to import the notion of care. Care does not offer control, but involves sustained and respectful tinkering towards improvement. Which is not to say in the end the tomatoes our informants care for are good. In the end these tomatoes get eaten. And while eating performs tomatoes as ‘good to eat’, it also finishes them off. Valuing may lead on to destruction. An important lesson for valuation studies indeed.

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