Articles
Characteristic $p$
methods in characteristic zero via ultraproducts, to appear
in
"Recent Developments in Commutative Algebra", Editors: M. Fontana, S.
Kabbaj, B. Olberding and I. Swanson, Springer(2009).
Constructible invariants, J. Algebra 304 (2006), 1059-1089.
M.
Aschenbrenner and H. Schoutens, Lefschetz extensions,
tight closure, and big Cohen-Macaulay algebras, will appear
in Israel Journal of Math.
Bounds in
polynomial
rings over Artinian local rings,
Monatshefte Math. 150 (2007), 249-261.
A local flatness
criterion for complete modules, Comm.
Algebra 35 (2007), 289-311.
Asymptotical homological
conjectures in mixed characteristic, Pacific
Journal of Math 230 (2007),
427-468.
Absolute bounds on the
number of generators of Cohen-Macaulay ideals of height two, Bull. BMS 13 (2006), 719-732.
Pure subrings of regular
rings are pseudo-rational, Trans. Amer.
Math. Soc. 360 (2008), 609-627.
Log-terminal
Singularities and Vanishing Theorems via non-standard tight closure, J. of Alg.
Geom. 14 (2005) 357-390.
On the vanishing of Tor
for the absolute integral closure,
J. Algebra 275 (2004), 567-574.
Canonical big
Cohen-Macaulay algebras and rational singularities, Illinois J.
Math. 41 (2004), 131-150.
Lefschetz Principle
applied to symbolic powers, J. of
Algebra and its Appl. 2 (2003),
177-187.
Non-standard tight
closure for affine $\mathbb C$-algebras, Manu. Math., 111 (2003),
379-412.
Projective dimension and
the singular locus, Comm.
Algebra 31 (2003),
217-239.
Mixed characteristic
homological theorems in low degrees, Comp. Rend. Ac. Sci. 336 (2003),
463-466.
Number of generators of a
Cohen-Macaulay ideal, J. Algebra 259 (2003),
235-242.
Computing the minimal
number of equations defining an affine curve ideal-theoretically, J. Pure
Applied Alg. 177 (2003),
95-101.
A non-standard proof of
the Briancon-Skoda Theorem, Proc. Amer.
Math. Soc. 131 (2003),
103-112.
J. Denef and
H. Schoutens, On the decidability of
the existential theory of $F_p[[t]]$, Valuation
Theory and its Applications, Vol. 2 (Saskatoon, 1999), 43-60, Fields
Inst. Commun., 33, AMS, 2003.
T.S. Gardener
and H. Schoutens, Rigid subanalytic sets, Valuation
Theory and its Applications, Vol. 1 (Saskatoon, 1999), 141-150, Fields
Inst. Commun., 32, AMS, 2002.
Recursive sequences and
flatness, Rocky
Mountain J. of Math. 31, (2001), pp.
1423-1427.
Uniform bounds in
Algebraic Geometry and Commutative Algebra, in
"Connections between Model Theory and Algebraic and Analytic Geometry"
(ed. A. Macintyre), Quaderni di Mathematica 6, (2000), pp.
43-93.
T.S. Gardener
and H. Schoutens, Flattening and
subanalytic sets in rigid analytic geometry, Proc. of
Lond. Math. Soc. 83 (2001),
681-707.
Artin approximation via
the model theory of Cohen-Macaulay rings, Logic
Colloquium '98: proceedings of the 1998 ASL Meeting held in Prague,
Czech Republic (S. Buss, P. Hajek and P. Pudlak), Lect. Notes in Logic,
13 (2000), pp.
409-425.
Bounds in cohomology, Israel J.
of Math. 116 (2000),
125-169.
Embedded resolution of
singularities in rigid analytic geometry, Ann. Fac.
Sci. Toulouse VIII (1999),
297-330.
Existentially closed
models of the theory of Artinian local rings, J. Symb.
Logic, 64 (1999),
825-845.
Rigid analytic
flatificators, Quart. J.
Math. Oxford Ser. (2) 50 (1999),
321-353.
The closure of rigid
semianalytic sets, J. Algebra.
198 (1997),
120-134.
Blowing up in rigid
analytic geometry, Bull. Soc.
Math. Belg. 2 (1994),
401-419.
Rigid subanalytic sets
in
the plane, J. Algebra 170 (1994), no.
1, 266-276.
Rigid subanalytic sets, Compositio
Math. 94 (1994),
269-295.
Uniformization of rigid
subanalytic sets, Compositio
Math. 94 (1994),
227-245.
Approximation properties
for some non-noetherian local rings, Pacific J.
Math. 131 (1988),
331-359.
