Nguyen, Kien Huu Uniform rationality of the Poincaré series of definable, analytic equivalence relations on local fields. (English) Zbl 1469.11478 Trans. Am. Math. Soc., Ser. B 6, 274-296 (2019). MSC: 11U09 03C60 03C10 03C98 11M41 11S80 20C15 20E07 × Cite Format Result Cite Review PDF Full Text: DOI arXiv OA License
Cubides Kovacsics, Pablo; Leenknegt, Eva Integration and cell decomposition in \(P\)-minimal structures. (English) Zbl 1428.03060 J. Symb. Log. 81, No. 3, 1124-1141 (2016). Reviewer: Paweł Gładki (Katowice) MSC: 03C64 03C07 03C10 12J25 12L12 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Cluckers, Raf; Leenknegt, Eva Rectilinearization of semi-algebraic \(p\)-adic sets and Denef’s rationality of Poincaré series. (English) Zbl 1154.14019 J. Number Theory 128, No. 7, 2185-2197 (2008). Reviewer: Christian Pierre (Louvain-la-Neuve) MSC: 14G20 11S80 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
du Sautoy, Marcus Counting conjugacy classes. (English) Zbl 1113.20025 Bull. Lond. Math. Soc. 37, No. 1, 37-44 (2005). MSC: 20D60 11M41 20E45 20G25 20H05 × Cite Format Result Cite Review PDF Full Text: DOI
Cutkosky, Steven Dale; Herzog, Jürgen; Reguera, Ana Poincaré series of resolutions of surface singularities. (English) Zbl 1076.14006 Trans. Am. Math. Soc. 356, No. 5, 1833-1874 (2004). Reviewer: Marko Roczen (Berlin) MSC: 14B05 13D40 × Cite Format Result Cite Review PDF Full Text: DOI
Cutkosky, Steven Dale Poincaré series of line bundles on varieties. (English) Zbl 1086.13004 Lakshmibai, V. (ed.) et al., A tribute to C. S. Seshadri. A collection of articles on geometry and representation theory. Basel: Birkhäuser (ISBN 3-7643-0444-8/hbk). Trends in Mathematics, 220-240 (2003). Reviewer: Keith Johnson (Halifax) MSC: 13D40 14C20 14F05 × Cite Format Result Cite Review PDF
Avramov, Luchezar L. Homotopy Lie algebras and Poincaré series of algebras with monomial relations. (English) Zbl 1031.13006 Homology Homotopy Appl. 4, No. 2(1), 17-27 (2002). MSC: 13D40 13F20 55P99 × Cite Format Result Cite Review PDF Full Text: DOI EuDML EMIS
Denef, Jan; Loeser, François Definable sets, motives and \(p\)-adic integrals. (English) Zbl 1040.14010 J. Am. Math. Soc. 14, No. 2, 429-469 (2001). Reviewer: Werner Kleinert (Berlin) MSC: 14G40 14G20 03C10 03C98 03C68 03C95 12E30 12L12 14G15 14G27 11G25 11S40 12L10 14F20 14G05 14G10 14J20 14F42 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Watanabe, Kei-ichi Hilbert-Kunz multiplicity of toric rings. (English) Zbl 1056.13502 Proc. Inst. Nat. Sci., Nihon Univ. 35, 173-177 (2000). MSC: 13D40 13H15 14M25 × Cite Format Result Cite Review PDF
Gasharov, Vesselin; Peeva, Irena; Welker, Volkmar Rationality for generic toric rings. (English) Zbl 0958.13004 Math. Z. 233, No. 1, 93-102 (2000). MSC: 13D40 13F20 14M05 × Cite Format Result Cite Review PDF Full Text: DOI
Denef, Jan; Loeser, François Germs of arcs on singular algebraic varieties and motivic integration. (English) Zbl 0928.14004 Invent. Math. 135, No. 1, 201-232 (1999). Reviewer: Roy Joshua (Columbus) MSC: 14E18 14E15 14B05 14P10 03C10 13D40 14F42 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Albis González, Víctor Samuel; Chaparro, Raúl On a conjecture of Borevich and Shafarevich. (Spanish. English summary) Zbl 1306.11092 Rev. Acad. Colomb. Cienc. Exactas, Fis. Nat. 21, No. 80, 313-319 (1997). MSC: 11R58 13A35 × Cite Format Result Cite Review PDF
Ufnarovskij, V. A. Combinatorial and asymptotic methods in algebra. (English. Russian original) Zbl 0826.16001 Algebra VI. Encycl. Math. Sci. 57, 1-196 (1995); translation from Itogi Nauki Tekh., Ser. Sovrem. Probl. Mat., Fundam. Napravleniya 57, 5-177 (1990). MSC: 16-02 16W50 17B05 20F18 17B70 16W30 16P90 17B37 13D40 16Z05 16R10 16U30 13P10 × Cite Format Result Cite Review PDF
Kustin, Andrew R. Huneke-Ulrich almost complete intersections of Cohen-Macaulay type two. (English) Zbl 0826.13015 J. Algebra 174, No. 2, 373-429 (1995). Reviewer: M.Miller (Columbia) MSC: 13H10 13C40 13D40 × Cite Format Result Cite Review PDF Full Text: DOI Link
Kustin, Andrew R. The deviation two Gorenstein rings of Huneke and Ulrich. (English) Zbl 0924.13015 Simis, Aron (ed.) et al., Commutative algebra. Proceedings of the workshop, ICTP, Miramare-Trieste, Italy, September 14–25, 1992. Singapore: World Scientific. 140-163 (1994). MSC: 13D40 13H10 × Cite Format Result Cite Review PDF
van den Dries, Lou Analytic Ax-Kochen-Ershov theorems. (English) Zbl 0835.03004 Algebra, Proc. Int. Conf. Memory A. I. Mal’cev, Novosibirsk/USSR 1989, Contemp. Math. 131, Pt. 3, 379-398 (1992). Reviewer: M.Yasuhara (MR 93i:03041) MSC: 03C10 03C60 13J15 13J07 13L05 12L12 × Cite Format Result Cite Review PDF
Macintyre, Angus Rationality of p-adic Poincaré series: Uniformity in p. (English) Zbl 0731.12015 Ann. Pure Appl. Logic 49, No. 1, 31-74 (1990). Reviewer: D.Busneag (Craiova) MSC: 12L12 03C10 13L05 14G20 × Cite Format Result Cite Review PDF Full Text: DOI
du Sautoy, Marcus P. F. Finitely generated groups, p-adic analytic groups, and Poincaré series. (English) Zbl 0724.22010 Bull. Am. Math. Soc., New Ser. 23, No. 1, 121-126 (1990). Reviewer: G.Rangan (Madras) MSC: 22E35 20F05 22E20 03C10 20E18 11M41 11S40 × Cite Format Result Cite Review PDF Full Text: DOI
Ufnarovskij, V. A. Combinatorial and asymptotic methods in algebra. (Russian) Zbl 0706.16001 Itogi Nauki Tekh., Ser. Sovrem. Probl. Mat., Fundam. Napravleniya 57, 5-177 (1990). Reviewer: P.Koshlukov MSC: 16-02 16W50 17B05 20F18 17B70 16W30 16P90 17B37 13D40 16Z05 16R10 16U30 13P10 × Cite Format Result Cite Review PDF
Popov, V. L.; Vinberg, Eh. B. Invariant theory. (English. Russian original) Zbl 0789.14008 Algebraic geometry. IV: Linear algebraic groups, invariant theory, Encycl. Math. Sci. 55, 123-278 (1994); translation from Itogi Nauki Tekh., Ser. Sovrem. Probl. Mat., Fundam. Napravleniya 55, 137-309 (1989). MSC: 14L24 14L30 14M17 14-03 14-02 20G05 × Cite Format Result Cite Review PDF Full Text: DOI
Popov, V. L.; Vinberg, Eh. B. Invariant theory. (Russian) Zbl 0735.14010 Itogi Nauki Tekh., Ser. Sovrem. Probl. Mat., Fundam. Napravleniya 55, 137-309 (1989). Reviewer: N.Andruskiewitsch (Bonn) MSC: 14L24 14L30 14M17 14-03 14-02 20G05 × Cite Format Result Cite Review PDF
Denef, J.; van den Dries, Lou \(p\)-adic and real subanalytic sets. (English) Zbl 0693.14012 Ann. Math. (2) 128, No. 1, 79-138 (1988). Reviewer: W.Lütkebohmert MSC: 14Pxx 14G20 × Cite Format Result Cite Review PDF Full Text: DOI
Denef, J. Multiplicity of the poles of the Poincaré series of a p-adic subanalytic set. (English) Zbl 0682.12013 Sémin. Théor. Nombres, Univ. Bordeaux I 1987-1988, Exp. No. 43, 8 p. (1988). Reviewer: F.Herrlich MSC: 11S80 12J25 32B20 14G10 11S40 × Cite Format Result Cite Review PDF Full Text: EuDML
Avramov, Luchezar L.; Kustin, Andrew R.; Miller, Matthew Poincaré series of modules over local rings of small embedding codepth or small linking number. (English) Zbl 0648.13008 J. Algebra 118, No. 1, 162-204 (1988). Reviewer: R.Fröberg MSC: 13D03 13H10 13C12 13C05 × Cite Format Result Cite Review PDF Full Text: DOI
Igusa, Jun-ichi Some aspects of the arithmetic theory of polynomials. (English) Zbl 0649.10016 Discrete groups in geometry and analysis, Pap. Hon. G. D. Mostow 60th Birthday, Prog. Math. 67, 20-47 (1987). Reviewer: S.Raghavan MSC: 11E45 11-02 11R42 12-02 11E76 14G10 × Cite Format Result Cite Review PDF
Zacharia, Dan Graded Artin algebras, rational series, and bounds for homological dimensions. (English) Zbl 0609.16001 J. Algebra 106, 476-483 (1987). Reviewer: J.L.Gómez Pardo MSC: 16W50 16P20 16E10 16Gxx 16P10 × Cite Format Result Cite Review PDF Full Text: DOI
Backelin, Jörgen; Roos, Jan-Erik When is the double Yoneda Ext-algebra of a local noetherian ring again noetherian? (English) Zbl 0592.13013 Algebra, algebraic topology and their interactions, Proc. Conf., Stockholm 1983, Lect. Notes Math. 1183, 101-119 (1986). Reviewer: R.Fröberg MSC: 13D03 13E05 18G15 13H99 × Cite Format Result Cite Review PDF
Denef, Jan p-adic semi-algbraic sets and cell decomposition. (English) Zbl 0584.12015 J. Reine Angew. Math. 369, 154-166 (1986). MSC: 11S80 13D03 12L12 03C10 14G20 × Cite Format Result Cite Review PDF Full Text: DOI Crelle EuDML
Jacobsson, Carl; Kustin, Andrew R.; Miller, Matthew The Poincaré series of a codimension four Gorenstein ring is rational. (English) Zbl 0575.13007 J. Pure Appl. Algebra 38, 255-275 (1985). Reviewer: R.Fröberg MSC: 13D99 13H10 55U35 13H05 13D03 × Cite Format Result Cite Review PDF Full Text: DOI
Backelin, Jörgen; Fröberg, Ralf Poincaré series of short Artinian rings. (English) Zbl 0572.13001 J. Algebra 96, 495-498 (1985). MSC: 13D03 13E10 13H15 13H10 × Cite Format Result Cite Review PDF Full Text: DOI
Kustin, Andrew R.; Miller, Matthew Classification of the Tor-algebras of codimension four Gorenstein local rings. (English) Zbl 0565.13004 Math. Z. 190, 341-355 (1985). MSC: 13H10 13D03 18G15 × Cite Format Result Cite Review PDF Full Text: DOI EuDML
Billington, Nicholas Growth of groups and graded algebras: Erratum. (English) Zbl 0558.20024 Commun. Algebra 13, 753-755 (1985). Reviewer: J.W.Cannon MSC: 20F05 20K99 16W50 20F10 13D99 × Cite Format Result Cite Review PDF Full Text: DOI
Billington, Nicholas Growth of groups and graded algebras. (English) Zbl 0547.20026 Commun. Algebra 12, 2579-2588 (1984). Reviewer: J.W.Cannon MSC: 20F05 20F10 13D99 16W50 × Cite Format Result Cite Review PDF Full Text: DOI
Denef, J. The rationality of the Poincaré series associated to the p-adic points on a variety. (English) Zbl 0537.12011 Invent. Math. 77, 1-23 (1984). Reviewer: J.Oesterlé MSC: 11S80 14G20 03C10 12L12 13H15 × Cite Format Result Cite Review PDF Full Text: DOI EuDML
Wilson, George V. Ultimately closed projective resolutions and rationality of Poincaré- Betti series. (English) Zbl 0547.13010 Proc. Am. Math. Soc. 88, 221-223 (1983). Reviewer: L.L.Avramov MSC: 13D03 13E10 16Gxx × Cite Format Result Cite Review PDF Full Text: DOI
Milne, J. S. Étale cohomology. (Ehtal’nye kogomologii). Transl. from the English. (Russian) Zbl 0544.14015 Moskva: Izdatel’stvo ”Mir”. 392 p. R. 3.80 (1983). MSC: 14F20 14-01 14-02 14B25 14G10 14F05 14G99 × Cite Format Result Cite Review PDF
Yamazaki, Tadashi Integrals defining singular series. (English) Zbl 0537.12012 Mem. Fac. Sci., Kyushu Univ., Ser. A 37, 113-128 (1983). Reviewer: M.van der Put MSC: 11S80 11N37 13H15 14G20 × Cite Format Result Cite Review PDF Full Text: DOI
Fröberg, Ralf Two notes on compressed algebras. (English) Zbl 0532.13012 Rep., Dep. Math., Univ. Stockh. 18, 5 p. (1983). MSC: 13H10 14M05 13C13 13H05 13H15 × Cite Format Result Cite Review PDF
Roos, Jan-Erik On the use of graded Lie algebras in the theory of local rings. (English) Zbl 0523.13010 Commutative algebra, Symp. Durham 1981, Lond. Math. Soc. Lect. Note Ser. 72, 204-230 (1982). MSC: 13H15 55P35 13D03 17B70 × Cite Format Result Cite Review PDF
Backelin, Joergen Les anneaux locaux à rélations monomiales ont des séries de Poincaré- Betti rationnelles. (French) Zbl 0518.13016 C. R. Acad. Sci., Paris, Sér. I 295, 607-610 (1982). MSC: 13H15 13J05 14M12 × Cite Format Result Cite Review PDF
Anick, David J. A note on the paper: ”A counterexample to a conjecture of Serre”. (English) Zbl 0507.55005 Ann. Math. (2) 116, 661 (1982). MSC: 55P35 13D03 57T25 13E05 57T05 × Cite Format Result Cite Review PDF Full Text: DOI
Fröberg, Ralf A study of graded extremal rings and of monomial rings. (English) Zbl 0498.13012 Math. Scand. 51, 22-34 (1982). MSC: 13H15 13D03 13H10 13E05 × Cite Format Result Cite Review PDF Full Text: DOI EuDML
Roos, Jan-Erik Homology of loop spaces and of local rings. (English) Zbl 0512.13015 18th Scand. Congr. Math., Proc., Aarhus 1980, Prog. Math. 11, 441-468 (1981). MSC: 13H99 13D99 55P35 13-02 55-02 13H15 57T05 16W30 57T25 × Cite Format Result Cite Review PDF
Balcerzyk, Stanislaw On minimal resolutions for some Artinian local rings. (English) Zbl 0494.13008 Bull. Acad. Pol. Sci., Sér. Sci. Math. 29, 15-20 (1981). MSC: 13H99 13D03 13E10 × Cite Format Result Cite Review PDF
Schoeller, C. Homologie d’anneaux locaux de dimension d’immersion 3. (French) Zbl 0493.13011 Seminaire d’algebre Paul Dubreil et Marie-Paule Malliavin, 33eme Annee, Proc., Paris 1980, Lect. Notes Math. 867, 212-233 (1981). MSC: 13H15 18G15 13D25 13D30 × Cite Format Result Cite Review PDF
Gulliksen, Tor H. On the Hilbert series of the homology of differential graded algebras. (English) Zbl 0461.13004 Math. Scand. 46, 15-22 (1980). MSC: 13D25 13H15 × Cite Format Result Cite Review PDF Full Text: DOI EuDML
Babenko, I. K. Analytical properties of Poincaré series of a loop space. (English) Zbl 0455.55006 Math. Notes 27, 359-367 (1980). MSC: 55P35 × Cite Format Result Cite Review PDF Full Text: DOI
Sally, Judith D. The Poincaré series of stretched Cohen-Macaulay rings. (English) Zbl 0449.13010 Can. J. Math. 32, 1261-1265 (1980). MSC: 13H15 13H10 13D03 × Cite Format Result Cite Review PDF Full Text: DOI
Rahbar-Rochandel, Hamid Sur la série de Poincaré de certains anneaux locaux noetheriens. (French) Zbl 0448.13016 Bull. Sci. Math., II. Ser. 104, 305-322 (1980). MSC: 13H15 13D03 × Cite Format Result Cite Review PDF
Babenko, I. K. Über analytische Eigenschaften Poincaréscher Reihen von Loopräumen. (Russian) Zbl 0447.55007 Mat. Zametki 27, 751-765 (1980). MSC: 55P35 × Cite Format Result Cite Review PDF
Ufnarovskij, V. A. Poincaré series of graded algebras. (English) Zbl 0446.16034 Math. Notes 27, 12-18 (1980). MSC: 16W10 16W50 17B35 × Cite Format Result Cite Review PDF Full Text: DOI
Milne, J. S. Étale cohomology. (English) Zbl 0433.14012 Princeton Mathematical Series. 33. Princeton, New Jersey: Princeton University Press. XIII, 323 p. $ 33.50 (1980). MSC: 14F20 14-02 14-01 14F05 14G10 14G99 14B25 × Cite Format Result Cite Review PDF Backlinks: MO
Ufnarovskij, V. A. Über Poincarereihen graduierter Algebren. (Russian) Zbl 0432.16018 Mat. Zametki 27, 21-32 (1980). MSC: 16W10 16W50 17B35 × Cite Format Result Cite Review PDF
Sakuma, Motoyoshi; Okuyama, Hiroshi On the Poincaré series of a local ring reduced modulo its socle. (English) Zbl 0498.13013 J. Math., Tokushima Univ. 13, 1-6 (1979). MSC: 13H15 13D03 13H10 13E05 × Cite Format Result Cite Review PDF
Schoeller, C. Rationalite de certaines séries de Poincaré. (French) Zbl 0453.13008 Semin. d’algebre Paul Dubreil, Proc., Paris 1977/78, 31eme Annee, Lect. Notes Math. 740, 323-384 (1979). MSC: 13D03 13H15 × Cite Format Result Cite Review PDF
Babenko, I. K. The Poincaré series of iterated loop spaces. (English) Zbl 0439.55004 Russ. Math. Surv. 34, No. 3, 193-194 (1979). MSC: 55P35 55Q05 × Cite Format Result Cite Review PDF Full Text: DOI
Avramov, Luchezar L. On the convergence radius of Poincaré series of local rings. (English) Zbl 0433.13010 Mat. Inst., Stockh. Univ. 4, 17 P. (1979). MSC: 13H15 13D03 13E05 × Cite Format Result Cite Review PDF
Serre, Jean-Pierre Un exemple de série de Poincaré non rationnelle. (French) Zbl 0427.55005 Indag. Math. 41, 469-477 (1979). MSC: 55P35 16S10 17B70 × Cite Format Result Cite Review PDF
Sjödin, Gunnar The Poincaré series of modules over a local Gorenstein ring with \(m^3=0\). (English) Zbl 0426.13007 Mat. Inst., Stockh. Univ. 1979, No. 2, 7 P. (1979). MSC: 13H99 13H10 13E10 13D03 × Cite Format Result Cite Review PDF
Avramov, Luchezar Sur la croissance des nombres de Betti d’un anneau local. (French) Zbl 0425.13009 C. R. Acad. Sci., Paris, Sér. A 289, 369-372 (1979). MSC: 13H15 13D03 55S30 13E05 × Cite Format Result Cite Review PDF
Roos, Jan-Erik Relations between the Poincaré-Betti series of loop spaces and of local rings. (English) Zbl 0415.13012 Semin. d’algebre Paul Dubreil, Proc., Paris 1977/78, 31eme Annee, Lect. Notes Math. 740, 285-322 (1979). MSC: 13H15 13H10 13E05 16W30 57T05 55P35 13D99 × Cite Format Result Cite Review PDF
Babenko, I. K. Über Poincaresche Reihen mehrfacher Loopräume. (Russian) Zbl 0411.55005 Usp. Mat. Nauk 34, No. 3(207), 191-192 (1979). MSC: 55P35 55Q05 × Cite Format Result Cite Review PDF
Fröberg, Ralf Some complex constructions with applications to Poincaré series. (English) Zbl 0411.13014 Semin. d’Algebre Paul Dubreil, Proc., Paris 1977/78, 31eme Annee, Lect. Notes Math. 740, 272-284 (1979). MSC: 13H10 13H05 × Cite Format Result Cite Review PDF
Backelin, Jörgen; Fröberg, Ralf Studies on some k-algebras giving the Poincaré series of graded k- algebras of length \(\leq 7\) and local rings of embedding dimension 3 with \(m^3=0\). (English) Zbl 0433.13009 Mat. Inst., Stockh. Univ. 9, 7 P. (1978). MSC: 13F20 13H15 13D03 13E10 × Cite Format Result Cite Review PDF
Golod, E. S. On the homology of certain local rings. (English) Zbl 0424.13008 Russ. Math. Surv. 33, No. 5, 185-186 (1978). MSC: 13H15 13D03 13D25 × Cite Format Result Cite Review PDF Full Text: DOI
Levin, Gerson Poincaré series of modules over local rings. (English) Zbl 0407.13020 Proc. Am. Math. Soc. 72, 6-10 (1978). MSC: 13H15 × Cite Format Result Cite Review PDF Full Text: DOI
Levin, Gerson Lectures on Golod homomorphisms. (English) Zbl 0439.13016 Mat. Inst., Stockh. Univ. 15, 73 P. (1976). MSC: 13H15 13D03 13E10 × Cite Format Result Cite Review PDF
Gusev, G. I. On Poincaré series for systems of maximal rank. (Russian) Zbl 0394.10011 Stud. in Number Theory, Saratov, Interuniv. Sci. Collect. 6, 33-37 (1975). MSC: 11D88 14G05 11E95 11A07 × Cite Format Result Cite Review PDF