25 research outputs found
On a reconstruction problem
No full textAbstractThis note supplements an earlier paper of this author, in which the concept of a strong k-hypomorphism between two graphs was defined (Thatte, 1990, Sectin VI). For k=1, this is just a hypomorphism. Here it is proved that strongly k-hypomorphic graphs and strongly k-edge hypomorphic directed graphs are isomorphic if k>1
Degree Extensions of Arbitrary Valuation Rings and "Best "
No full textWe prove the explicit characterization of the so-called "best f" for degree
Artin-Schreier and degree Kummer extensions of Henselian valuation
rings in residue characteristic . This characterization is mentioned briefly
in [Th16, Th18]. Existence of best is closely related to the defect of such
extensions and this characterization plays a crucial role in understanding
their intricate structure. We also treat degree Artin-Schreier defect
extensions of higher rank valuation rings, extending the results in [Th16], and
thus completing the study of degree extensions that are the building blocks
of the general theory.Comment: 13 page
Ramification theory for degree p extensions of arbitrary valuation rings in mixed characteristic (0, p )
No full text
A reconstruction problem related to balance equations II: The general case
No full textAbstractA modified k-deck of a graph G, first introduced in (Krasikov and Roditty, 1987), is obtained by removing k edges of G in all possible ways, and adding k (not necessarily new) edges in all possible ways. Krasikov and Roditty asked if it was possible to construct the usual k-edge deck of a graph from its modified k-deck. In (Thatte, to appear), the author solved this problem for the case when k = 1. In this paper, the problem is completely solved for arbitrary k. The proof makes use of the k-edge version of Lovász's result and the eigenvalues of certain matrix related to the Johnson graph
Upper Ramification Groups for Arbitrary Valuation Rings
No full textT. Saito established a ramification theory for ring extensions locally of
complete intersection. We show that for a Henselian valuation ring with
field of fractions and for a finite Galois extension of , the
integral closure of in is a filtered union of subrings of which
are of complete intersection over . By this, we can obtain a ramification
theory of Henselian valuation rings as the limit of the ramification theory of
Saito. Our theory generalizes the ramification theory of complete discrete
valuation rings of Abbes-Saito. We study "defect extensions" which are not
treated in these previous works.Comment: 44 page
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Ramification Theory for Arbitrary Valuation Rings in Positive Characteristic
No full textOur goal is to develop ramification theory for arbitrary valuation fields, that is compatible with the classical theory of complete discrete valuation fields with perfect residue fields. We consider fields with more general (possibly non-discrete)
valuations and arbitrary (possibly imperfect) residue fields. The “defect” case, i.e., the case where there is no extension of either the residue field or the value group, gives rise to many interesting complications. We present some new results for Artin-Schreier extensions of valuation fields in positive characteristic (\cite{V1}). These results relate the ``higher
ramification ideal" of the extension with the ideal generated by the inverses of Artin-Schreier
generators via the norm map. These are further related to K\" ahler differentials, which has been
shown in previous work of Kato and others to offer refined information about wild ramification
in the imperfect residue field case. We also introduce a generalization and further refinement of Kato's refined Swan conductor in this case. Similar results are true in the mixed characteristic case (\cite{V2})
Fault Diagnosis of Semiconductor Random Access Memories
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Reason: Restricted to UIUC communityOpen Restriction set for Item 100821 on 2019-11-15T17:33:23Z with date null by [email protected] Services Electronics Program / DAAB-07-72-C-0259OpenCoordinated Science Laboratory was formerly known as Control Systems Laboratory"Author name appears as ""Satish Munkund Thatte"" in front matter
