A note on the use of Frobenius map and D-modules in local cohomology

References

• Björk, J. E. (1979). Rings of Differential Operators. Amsterdam: North-Holland Publishing Company, New York: Oxford.
   Google Scholar
• Blickle, M. (2001). The intersection homology D-module in finite characteristic. Ph.D. Thesis. USA: University of Michigan.
   Google Scholar
• Bourbaki, N. (2006). Éléments de Mathématique. Algébre Commutative, Chapters 8 et 9. Berlin, Heidelberg: Springer-Verlag.
   Google Scholar
• Brodmann, M., Sharp, R. Y. (1998). Local Cohomology: An Algebraic Introduction with Geometric Applications, Vol. 60. Cambridge: Cambridge University Press.
   Google Scholar
• Coutinho, S. C. (1995). A Primer of Algebraic D-Modules, London Mathematical Society Student Texts, UK: Cambridge University Press.
   Google Scholar
• Eghbali, M. (2013). On Artinianness of formal local cohomology, colocalization and coassociated primes. Math. Scand. 113:5–19.
   Web of Science ®Google Scholar
• Eghbali, M. (2014). On set theoretically and cohomologically complete intersection ideals. Canad. Math. Bull. 57(3):477–484.
   Web of Science ®Google Scholar
• Eghbali, M., Schenzel, P. (2012). On an endomorphism ring of local cohomology. Commun. Algebra 40:4295–4305.
   Web of Science ®Google Scholar
• Grothendieck, A. (1967). Local Cohomology,Lecture Notes in Mathematics, Vol. 41. Heidelberg: Springer.
   Google Scholar
• Grothendieck, A. (1968). Cohomologie Locale des Faisceaux et Théorèmes de Lefschetz Locaux et Globaux (SGA 2). Advanced Studies in Pure Mathematics 2, Amsterdam: North-Holland Publishing Company.
   Google Scholar
• Hartshorne, R. (1968). Cohomological dimension of algebraic varieties. Ann. Math. 88(2):403–450.
   Web of Science ®Google Scholar
• Hartshorne, R., Speiser, R. (1977). Local cohomological dimension in characteristic p. Ann. Math. 105(2):45–79.
   Web of Science ®Google Scholar
• Hellus, M., Stückrad, J. (2008). On endomorphism rings of local cohomology modules. Proc. Am. Math. Soc. 136(7):2333–2341.
   Web of Science ®Google Scholar
• Hochster, M., Huneke, C. (1989). Tight closure and strong F-regularity. Mém. Soc. Math. France (N.S.) 38:119–133.
   Google Scholar
• Hochster, M., Huneke, C. (1994). Indecomposable canonical modules and connectedness. In: Heinzer, W., Huneke, C., Sally, J., eds. Commutative Algebra: Syzygies, Multiplicities, and Birational Algebra, (South Hadley, MA, 1992) Contemp. Math., Vol. 159, pp. 97–208.
   Google Scholar
• Huneke, C., Koh, J. (1991). cofiniteness and vanishing of local cohomology modules. Math. Proc. Cambridge Philoos. Soc. 110(3):421–429.
   Web of Science ®Google Scholar
• Kunz, E. (1969). Characterization of regular local rings in characteristic p. Am. J. Math. 91:772–784.
   Web of Science ®Google Scholar
• Lyubeznik, G. (1993). Finiteness properties of local cohomology modules (an application of D-modules to commutative algebra. Invent. Math. 113(1):41–55.
   Web of Science ®Google Scholar
• Lyubeznik, G. (1997). F-modules: An application to local cohomology and D-modules in characteristic p>0. Journal für reine und angewandte Mathematik 491:65–130.
   Web of Science ®Google Scholar
• Lyubeznik, G. (2000). Injective dimension of D-modules: A characteristic-free approach. J. Pure Appl. Algebra 149:205–212.
   Web of Science ®Google Scholar
• Lyubeznik, G. (2006). On the vanishing of local cohomology in characteristic p>0. Compos. Math. 142:207–221.
   Web of Science ®Google Scholar
• Mahmood, W., Schenzel, P. (2012). On invariants and endomorphism rings of certain local cohomology modules. J. Algebra 372:56–67.
   Web of Science ®Google Scholar
• Milne, J. S. (1980). Étale Cohomology, Princeton Mathematical Series, Vol. 33. USA: Princeton University Press.
   Google Scholar
• Ogus, A. (1973). Local cohomological dimension of algebraic varieties. Ann. Math. 98(2):327–365.
   Web of Science ®Google Scholar
• Peskine, C., Szpiro, L. (1973). Dimension projective finie et cohomologie locale. Publ. Math. I.H.E.S. 42:323–395.
   Google Scholar
• Schenzel, P. (2007). On formal local cohomology and connectedness. J. Algebra 315(2):894–923.
   Web of Science ®Google Scholar
• Schenzel, P. (2009). On endomorphism rings and dimensions of local cohomology modules. Proc. Am. Math. Soc. 137:1315–1322.
   Web of Science ®Google Scholar
• Schenzel, P. (2010). Matlis duals of local cohomology modules and their endomorphism rings. Archiv Math. 95:115–123.
   Web of Science ®Google Scholar
• Smith, K. E., Van den Bergh, M. (1997). Simplicity of rings of differential operators in prime characteristic. Proc. London Math. Soc. 75(3):32–62.
   Web of Science ®Google Scholar