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SUMMARY:Graded components of local cohomology modules supported on $\\math
frak{C}$-monomial ideals.
DTSTART;VALUE=DATE-TIME:20230202T103000Z
DTEND;VALUE=DATE-TIME:20230202T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T092230Z
UID:indico-event-8785@cern.ch
DESCRIPTION:Abstract: The structure of local cohomology modules is quite m
ysterious owing to their non-finite generation. Over the last three decade
s\, researchers have extensively investigated if they behave like finitely
-generated modules. Let $A$ be a Dedekind domain of characteristic zero su
ch that its localization at every maximal ideal has mixed characteristic w
ith finite residue field. Let $R=A[X_1\, \\ldots\, X_n]$ be a polynomial
ring equipped with the standard multigrading and let $I\\subseteq R$ be a
$\\mathfrak{C}$-monomial ideal. We call an ideal in $R$ a \\mathfrak{C}$-m
onomial ideal if it can be generated by elements of the form $aU$ where $a
\\in A$ (possibly nonunit) and $U$ is a monomial in $X_i$'s.\nLocal cohom
ology modules supported on usual monomial ideals of a polynomial ring over
a field gain a great deal of interest due to their connections \nwith com
binatorics and toric varieties. The objective of this talk is to discuss a
structure theorem for the multigraded components of the local \ncohomolog
y modules $H^i_I(R)$ for $i \\geq 0$. We will further show that if $A$ is
a PID then each component can be written as a direct sum of its \ntorsion
part and torsion-free part. This result evinces the finiteness of their Ba
ss numbers. This is joint work with Tony J. Puthenpurakal.\n\nhttps://indi
co.tifr.res.in/indico/conferenceDisplay.py?confId=8785
LOCATION: AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=8785
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