Commutative Algebra Seminar 

Fall 2006



Seminars will be in  Avery 351, and will be held twice a week:


Wednesdays 3:30 - 4:20 pm


Thursdays  2:30 - 3:20 pm



6th and 7th December (Wednesday and Thursday). Janet Striuli, UNL.


Title: G-covers of residue fields of local rings, I and II.



4th December (Monday) Irena Peeva, Cornell University.


Time and Room: 3:30 -- 4:30 in  Avery 112


Title: Hilbert Series



30th November (Thursday) Joseph Gubeladze, San Jose State University.


Title: K-theory of monoid rings


Abstract: 


All nontrivial elements in K-groups of monoid rings over regular rings are annihilated by

iterations of the natural Frobenius type endomorphisms. This is a higher analog of the

triviality of vector bundles on affine toric varieties. In the talk I will assume no

K-theoretical background: the main K-theoretical concepts will be presented in an informal

and completely accessible way, without giving a single formal definition.



29th November (Wednesday) Lars W. Christensen, UNL.


Title: Descent of semidualizing complexes for rings with the approximation property


22nd and 23rd November. Give thanks.


 


16th November (Thursday). Kevin Knudson, Mississippi State University.


Title: Algorithms in Discrete Morse Theory


Given a finite simplicial complex K and a real-valued map f on the vertices of K, we show

how to extend f to a discrete Morse function on all of K in such a way that the

corresponding discrete gradient mirrors the large-scale behavior of f.  We also present a

parametrized version of this problem.  Several examples and applications will be

discussed.



15th November (Wednesday) Hans-Bjoern Foxby, University of Copenhagen, Denmark.


Title: Intersection Theorems and Small Dimension


Abstract:


The New Intersection Theorem (NIT) by Peskine & Szpiro, Hochster, and Roberts and its

extensions will be compared to those of the Improved NIT by Evans & Griffith. This is

joint work with Yassemi.



13th November (Monday) Hans-Christian Herbig, University of Frankfurt, Germany.


Time and Room: 3:35 -- 4:30, in Avery 112


Title: A homological approach to singular reduction in deformation quantization



9th November (Thursday). Math Day. (No seminar)



8th November (Wednesday) Anders Frankild, University of Copenhagen, Denmark.


Title: When is a finitely generated module complete?


Abstract:


Motivated by work of C. U. Jensen, R.-O. Buchweitz, and H.  Flenner, we prove the

following result:


Let R be a commutative noetherian ring and I be an ideal in the Jacobson radical of R. Let

R^ be the I-adic completion of R. If M is a finitely generated R-module such that

Ext^i_R(R^,M) = 0 for all i >0, then M is I-adically complete.


One may think of this as a functorial way of detecting completeness of finitely generated

modules. This is joint work with Sean Sather-Wagsatff.



2nd November (Thursday). Sylvia Wiegand, UNL.


Title: Sums of 2 units and almost diagonal matrices



1st November (Wednesday) Andres Rosenschon, University of Alberta, Canada.


Title: Algebraic cycles on products of elliptic curves over p-adic fields.


Abstract:


We give examples of smooth projective varieties X over p-adic fields such that for

suitable l the Chow group in codimension 2 modulo l is infinite. This is joint work with

V. Srinivas.



31st October (Tuesday), around 9:30 AM. Srikanth Iyengar, UNL. (This is not a seminar)


Title: Support of Koszul homology modules and positivity of Euler characteristics



26th October (Thursday). Zach Teitler, South Eastern Louisiana University.


Title: The intersection of the curves through a set of points in P^2


Abstract:


Given a set of points in the projective plane P^2, we consider the intersection of the

degree-d curves through the given set of points. This has applications to the computation

of the multiplier ideals of the original set of points. By using the Hilbert-Burch

theorem, we can "predict" what dimension and degree the intersection will have in terms of

the geometry of the given set of points; and we can show that for most arrangements of

points, these predictions come true.



25th October (Wednesday) Winfried Bruns, University of Osnabrueck, Germany.


Title: On the coefficients of Hilbert quasi-polynomials



18th and 19th October. Rest Cure.



12th October (Thursday). Chuck Weibel, Rutgers University.


Title: Hochschild homology and its cdh cousin describe K-theory of polynomials


Abstract: 


We show that the groups NK_0(R), which describe projective modules over R[t] modulo

projectives over R, are direct sums of copies of cdh Hochschild homology except that the

seminormalization R+=H^0(R,O) is replaced by R+/R. Higher K-groups are direct sums of the

usual Hochschild homology groups. Thus many open questions in K-theory and Hochschild

homology are more closely related than we thought.



11th October (Wednesday) Hamid Rahmati, UNL.


Title: Contracting Endomorphisms and Gorenstein modules


Abstract:


We characterize Gorenstein modules when then ring has a finite contracting endomorphism.



4th and 5th October.  No seminars.



27th and 28th September (Wednesday and Thursday). Roger Wiegand, UNL.


Title: Extended modules


Abstract: 


Let (R,m) be a local ring, S a Noetherian ring and R--> S a faithfully flat extension.

Given a finitely generated S-module N, when is there a finitely generated R-module M such

that S\otimes_R M \cong N (or, more generally, a finitely generated R-module M such that N

is isomorphic to a direct summand of S\otimes_RM)?  I will discuss these questions in

special cases, with particular emphasis on the case where S is the Henselization or

completion of R.


The talks will be partly a survey of known results, with some proofs when they are fun.

The talks should be accessible to graduate students.



20th and 21th September (Wednesday and Thursday). Mara Neusel, Texas Tech.


Title: Some things about invariant theory



14th September (Thursday). Rodney Sharp, University of Sheffield, U.K.



Title: Uniform behaviour of Frobenius closures of parameter ideals



13th September (Wednesday). Diana White, UNL.


Title: G_C projective dimension


Abstract:


In this talk, we introduce and investigate the notion of G_C-projectivity for modules over

(possibly non-noetherian) commutative rings, where C is a semidualizing module.  This

extends the notion of G_C projectivity to the non-noetherian setting and generalizes

projectivity and G-projectivity within this setting.  We then study the resulting modules

of finite G_C-projective dimension, showing in particular that they admit

G_C-projective approximations a' la Auslander and Buchweitz.




6th and 7th September (Wednesday and Thursday).   Lucho Avramov and Srikanth Iyengar, UNL.


Title: A class inequality for differential modules



30th and 31st August (Wednesday and Thursday). Greg Piepmeyer and Mark Walker, UNL.


Title: A "new" proof of the New Intersection Theorem


Abstract:


We give a proof of Roberts' New Intersection Theorem in the mixed characteristic case that

uses Adams operations (as developed by Gillet-Soule) in lieu of the local Chern characters

used by Roberts.



24th August (Thursday). Ryo Takahasi, Meiji University, Japan.


Title:  Uncountably many indecomposable totally reflexive modules


Abstract: 


Several years ago, Huneke and Leuschke gave a theorem which proved a conjecture of

Schreyer.  It asserts that an excellent Cohen-Macaulay local ring of countable

Cohen-Macaulay type which is complete or has uncountable residue field has at most a

one-dimensional singular locus.  In this talk, I will verify that the assumption of the

excellent property can be removed, and consider the theorem over an arbitrary local ring.

I will prove that the existence of a certain prime ideal and a certain totally reflexive

module implies the existence of an uncountably infinite number of isomorphism classes of

indecomposable totally reflexive modules.



3rd August (Wednesday). Mark Rogers, Missouri State University.


Title: Gorenstein rings and irreducible parameter ideals


Abstract:



24th July (Monday).  Jung-Chen Liu, National Taiwan Normal University.


Title: Buchsbaum-Rim Multiplicites as Hilbert-Samuel Multiplicities



Maintained by  Srikanth Iyengar